Tamaz zerekiZis konspeqti saganSi "maTematika ekonomistebisaTvis" eleqtronul versia s ( − da misTanebisaTvis ) damatebuli aqvs "e leqtronuli sarCevi". konspeqti Zalze SekumSulia da Seicavs aucilebel masalas (orive semestrisaTvis) . amas garda is arasrulicaa — ar Seicavs analizuri geometriis sakiTxebs (pirveli semestris masalis nawili) . leqciebze masala gadmocemuli iqneba silabus is TanmimdevrobiT, rac zedmiwevniT ar daemT x veva konpeqtisas — saWiroa saleqcio Canawerebis regularulad keTeba keTeba da masalis S eswavla am C anawerebiT , konspeqtiT da im literaturiT , romelic silabusSia miTiTebuli. maTTan erTan sasargeblo iqneba , paralelurad, sxva koleg ebi s mier Se dgenil i kon speqt eb iT paralelurad sargebloba , iseve rogorc nebismieri wigni umaRles maTematikaSi , TqvenTvis misawvdom nebismier enaze. uamrav sasargeblo masala a i nternetSi . praqtikul mecadineobebzec SeiZleba Teoriuli masalis Sesaxebac kiTxvebis dasma, Tu isini maSin mimdinare praqtikul sakiTxeb Tanaa uSualod kavSirSi — pedagogebi gipasuxeben, Tu dro amis s aSualebas miscems maT , praqtikumis msvlelobisas . saerTod, garkveuli momentidan , romelic gecnobebaT, regularulad Ca tardeba konsultaciebi ; maSin morige profesors dausvamT nebismier SekiTxvas. (satitulo gverdi da eleqtronuli faili moamzada niko guniam) i astlhfllf(J , d.ff!hntftT!.f u.sbJJ6n, rnJ.JSJi/flJ6n CJf1hnLrJ6 ~ J c.. 7 shmJ'JrJ0rn35bn //!Jhn(!t1f1!J bSDn{f) (!JSC::soJO':JC' .JcnJJJ5f!(J)J iJnJliJ3r!!'JL JJtf'/)(J1!'fI MC:"Jd.J. dJlf!>fI!-J[, !>rnJC'flL ttfhn JmOJd()b h.J77Jf?.Jbmd.JJ In, iJ3J1f!Janu J}Jm~J;;mdJ jn n} _'6rnc='J3J /fJX/; nnoflu dJf!!>nLffl· . (}JtfhmfnLJ flu .)(!!'Jd:J6tfn , hmdJe!){j fldyrn ~.Ja.J L- '.:J!>n Dt!!Jr)jrnbnU': (OJ j-:Jhn LJ)Jtfnt JS~JjJJ07JbJJ ~3:J'J{!"JaJ)()3) a ij -om J(!'n6ndfl.JaJ- dJo.;/.;.:-t::>..:cJ, /1)):11 hnanL Jstf!Jn/riJ .fiji- LsbJ all all' -. ~fh) A = ~11. ~12.': .a 2h . {lm2 ... (lmn . ( Q m1 t]}'J 177 = n , JJon5 dJ!fJMlfb .:J3.r~hJ!fJt!!'n Jbrn(?20J - DSr3ns!?JC' c":I!'!YJ/Y[ dJJl;;-,.; dO? J 3.shn r!?J JhJ()OJJ]Jhn (Pf15orr0S(!!1j(}-, : a · . A 12 U 21 JJlfhn!J'!J JbmeXJ (!J nJam D JI!!' ~ h 17 , (/I'J dflun )JJ(!'1J :Jf!lJJJ6J!n ) OsneJ J(J}Jj.Jh ~f'..56rrOJr. £J J)mOjJ6nUJ , !] j(!!'nIJ 1:PmenJ· ~().samr;Sf!T'j!Jn dJIf/)nlYfI OJndr!!'JdJ .s!JJ J:snbJhmt DtJtJ? (!JnsJmo-5(!!'':Jh dst!Mtlt, hmJC!'niJ d07JJ.s!> t?rJJarn6JcgJ d(?t3md/l (/)()tfYr1JjcYJ JE' JJJf)iA , j -n!J fn1(1!'{)J, J h (JJJ ttl (!!}m 3 SD 11 ;in!hniJ'fl JCfll(!?jJJ' J!J(J))'YE'rnJJIJ JJtfhfllf0 ~ Jtrn olf) JC J6rl {je.J3 CJ· J. n . E ( i i. 0 ) o °1 . JJ!}(M')(J)0rn3.;6 dJiJnn/fb J !JmJf!!'n0 JJJC'J )C!'JdJ;;!fn O-nb tfmt':!'!JJ ? D :Y(!T'mJ.Jbn J.;L! fJnUlI iJ:3nJ. o'.J(}!'fTJ3.:o JJJ!mift 0 JUnOln Jc:'Jbn{}OJ]()7' dJo.5iJ.JC?JdJ' 0 0 ... 0) 0= ( ??':'.~ o 0 .. ·0 . A ~J ':;"f-.''':.r:J ffhJSdmonhJo';1C'f) Jbfn(!JJaS (JtJ01 JJtf!>/Jift] !>mJJE'()/! O(}f)C'JOJ A d,' .J,~()J./n {;.:2J5, 01':] c~!J b. .p~n~;mc:.JL (!JJ30Jhm uJJl!J6JC;; J UJJdJJi- jn ttfhn}moJa';l? - A d.. :lPIJ(Jjfr-i !/hJOb 2 ]mon!u3'Jcnn JJlfnnt/n AT unJ2mC"fTI:m JC'fJcri'JoJ3J' J. fJ· au a 2f ··· a mr \ A.,. = (l,Z a 22 (Jrnz ) arm (l.2fJ··· a mn /· ]~ (JlOJn!Jn /)nan!J OJ!I(J)}')m!YnJJ6n J<ftlhfJtrJJnr; QJdn 2;!JnuJ6(!} 3/))a,,\ d.11Y JZJn !f(77[!7'rTl6n (!' ( .a~f ~.: 0:(1) t-(BI.':. g~n '\ = (aAiI' a in + Sin \ ami' . 'ClmfJ B mf ,· . D mn ) I, Om/B m1 ,·· Umni-tmnj; dnfnncNJ lYJ!fb~f6J 5JJ)v)C'n JJfirLdlJ(!lJItJJJ JlJ: K ( ~t:'" : ~{~ )::: ( ~ ~/!' :. ~ ~(!) ) am 1 . Umn k 0lnt' ..Ka tnh ' dJ!!MLOdnL, lJbJJrnJJ A -!3 d.Jd2Mc:YlJ dJIJJb.i2031vn0J hrnJm!JiY A -+- (-I) (J . ]mdJJ(J) 1 A J!Jn!.J !Tl x/; !)fJdnL )Jtf!JrJ!I() 1 8 j() fl X K JJnanu· 6Jdk!3e'!J A ·8 oJ6n w<6csl-illJ hmOrn/l1J fJtJO")() Inx K AnanL C (JJJf!!Jrw'n 7 hrndr:!!'rJL e L ) )enJd.:Jo!:l!J1 JJJm/;J{J7 J(!}'J(!;lSr3 A dsf/vlifnL L -'.Jhn uf!'lyjjrr£n[ Je:'JdJ£l!JJn '!f[;e,; .3J3.5dlJ)C1ndJ 8 dJ1f!l()!fnu j -jnn t3Jt!nu fJJoJoJJnu J(!r'JJ.J6J.J2/l;.) ~.f J()(!'J(b!!!'fJ SJd),JJ&J2rJ W3j/]nCm07. J. (). Cij := (li1 Bt j + [ti2 g2 j +".f- U Ln B nj . ,rr:'3n~n dJbJdf,SJJfJJ, nm,J A. E = E· A := A. dJ36fJd&n(j) aJ~J JdriJ 1 hmo JJf!Jhm.iJJnL dJj/)JdnLJ [3.5 t3.J.Jh5JcfJnL, mJJhJEfn.Jdnbm3nL, !?JJr:J(!"()J !JJ.JEiJ nu dnh()07JC? n jJ&-r.!Y7 nSII hnLrD3J6nu c}jJh.JdnbJ (!J.I aJdAiM!!'Jd()u rnfJnJL/nJ6()Um!Jf)L ,,aJh(!Jj asJhJJc:nJd()L Jflc}JAOl 2ft:?s5JL!'JC'Ja.rC?mdnu JSbmontJ ' J·n· !JJ~fha.J(!Jmc?· A ·8 -:t B· A. C:'2JfJhJn5J5tf(l dJ[)()!J.!6C)/uOJ Jbl7lC'l7?~ 33.J(!?!Jv'ff:y(!;'() dJJfMifJ{3()bm)nL C?J ()2£J s!J(): Jd (J,ff?hn!ffJu J(!}' J/lJ5tfJO()t /';/)':)Jf!' .fO(I07 J.JhnJ':J{!!y) D:JIJ)OI 'lJJeaj6(}C!'() m f) if bJ (). A (}sffnf1!f(Ju rYJlfJhJnoJfJ!fn J!J(]J- .Jh(J)n 'd.)3r?.Jdn unJ3m(!;'fTI(f)() Jc.nD()(;!J:JOJ: det (AJ ) J A!. C!JffJ/JJnfJ.;ot!nu aso1JJg(}Y!fJ!J JrM&7m tn[;.ILbJn dJJrn3()(!'mm JJf!?J5S1/3C'.JdfJIJJ (!JJ J()/..;() e:'Jb- jJ£ tf7rJJf)J3rJL /Jlif2do(}. innJ.JC!:'() h.. 5Jtf:JIJJ0''Yhn hmrb3nWt3Jb dJf!JJJb()t!'() BJ t!' J E J If) f!!J:JOJ J5m C:]3 j nUJ(J) ~ sC'soJo':)C!' !JnJhJ3C'J/.;, !>I7?JJ(!!'!I!J ( I) 2 ') ... } 11) un JAf) (!!!!J!J.Jd.sO d.JndC!'.J a) 355ubJJ 3~Jatn (3JIJ J6tncnmr:> J(!" JJJIi!fmu ~.Ie:" JaYJnL, !l()d()O)· 3mp.'J3f){}) , IlmJ dS(J.5f).51f3(!!'JaJ'Jn !J1/>f) .J(!!'.JJJ5l!n dd5()0 fl53 J h Uf) JU ,0'] [Of)(?() J(!T'J!1JEtln jl7Jhrn onD r?JJ!J 3()(f?hJ Jst!snJ. nJC?J6.5Lf3(!!1JdJU J6mC?J3J j J Ii 1f(J, 0') d<fU'd/") noJJnu()J[J)J !JJm~.J,5rnaJ 3J5tf()J ) !Jm f!:'rn Sn6JJc:d~Ja CbJm63J?JJ 'Jf) Jb(n~ J a J C'':)O!-j. JJoJCf)(J)J~ 1 ,JJ~JOJif3C!'.J(}J (~) f 1;]) jJotfn<J} hsc?JJ5 /!Jbd() nb3.JIJ 3 unJL JJ5f1JD 2 (!J.J j ,!Jfn(!!1fT) t3~JlJJLfJC!'J(;.J (2) 3, i) (!'1':)6()J , ilj~C35f)Ji/ JJI/Jn 23sjjiJ mnn n!J3:Jhwu J Imdf!"JdUJlJ' jJ5NO 2~.J j , J ~J j OJbJflonC!'t7lOl n -'Jnn nfJ{3n/; JJJ(!!/)J tJ'J{!!YJ JJLP!JnL!n {Lff fh2'" {L,n '\ 0 A ~2: a~2 ._(12~ ) "0 ~nt a n2 · . (2nn / 0 Z;J[;3,"DnE(n(J) JJ JJfflv'lU'n!.J )(!!'Jo.J(;ff.JOnb.fJ.fb d.J@aJ!)()(!!'fl J3.J0'S nt2(J)f) SJdnJJ(,O~n, hmJc."'JaWLf J:/?JOl (JJJr:?J3n mAn (J)]nu:J3J: j) {/)(}tfJrru::J[!!' 1JJ000J(I!'Jfl .5hfi!.J f6':JudJf!J n- i/JC'fJ (f)JDJJJJhJ3f: (), 2'; 07(}[f)frlJ':)(2'1 6J&3COn JmoJ6nC!l.Jrr0!J ~ ':!/.;tfJ(!J J!Jmf7 fJ7.;IiJJJMJJC!'() .'J(T)jJ(2f'(} iJ!fl>n}rnl)r}(3Sb tP.J g';J/;f!J(!J.J\1J() OJJbJdJdNJC!:'f) j(l)3.J0'() !J3Jtf/l!?Jr;· j~JnC!'f) :'7.JwdI7SJ3()J, hmJ sU.J(f)n 6J&JJft>.i2n J~l.i3rnaJr; 0 (J)() (flJ"(L)!j t!" J IJ.1 (f) OJ;) A J J t:' an f.:J J 3 .f (!!1J am [J) tJ)JW J J diu 3 (!!' .J J() :in A 3 J (!Y' (1 fi[ (!J xl LJ 3fJu M(!?flL dnb.'Jt'?3f)[J)) Jon· Jf)3!y.J(Jj tJDJ; Utj " .. ~ . . oJb3nbnC!'fndl :l . a 2J · 2. .iJ n JJrrf,J nDt3:Jd/;JJ()6JdJD d:J(5l2:)M(fpf) 2J~..fE.f1Y3t!."'.10.J (j1 1 J 1"', Jr.J. (J)'j Jb JJC?J 2 bJif]f!',J?JJ t:':J/fflJ I JJ bJJIlJ.Jt!!'D tE.rJ';J/;'..i>mtfJ 6f)'(jcf[;() ,,+'1, t!Jrn(!!'rn (JJ:J j£!n, f)JJ~J3(L r:?JJ':Jb:JNn01 Dn8.f5n 11- ~ J J if hni/niJ (?:J if:J h ,3 n 5 J 5 t! n :Jbm{?.J6J Y3J(!!' J Ju:JJJn 5.JdnJ3(!T'J6nL 5..5 JIJ ; U J(9 J if (J)()(f)m::'Y(!f1n 5.JJliJ]{!!'n J{!}:J6':J(!!'nJ OJ.J3nun3J 5n7JonOl. !hml)'] ))n3n0 (!?.JIf.Jh3noJDtfiJ Ji3L !JJbJ aj1 a{2 a 21 O-Z'2.t 2n!Jn J~JJ:JlJtPi2JnL/2Js5 'JJnde:':J6J 'd.JtE2JiJ rtJ.JdmmJc;b:Jh()(!f'() (})!Jf)b23:JGn[ JjmbJ rnhn oJ2!u.JEn; Ov f1 C0.2 (!JJ a/ 2 ~j" jnh3.J{!!}() f)fi(!!JjiJ~B() t:JJ3.J t!!.J/!!'SJJ6:X!!YIJ M(!>(Ju Jnb:JrP3n(f). 2J1J3()on{!!"'ml1J J.JrnflJ n&2.JJ!.J.Jdnwa.Jf; dJrpJ:JMc:n(J 2JrP.5DJif3C:"JdJJn: (j,2) {?J (2,:0. inh?J2C!'n dJ{J):J..f!)n CJT1':":!D(]J1 dJrrIIJ j(l jJ[;!fJ() JdfJ,fmJ jj7iJJJ(I!1 SJ2ns3C!'/.; J.:J5JOJ 5n'lJJ5n II T U ) d.Jmlvu j() - OndJbn n - c/. JdmJrnJ I au 012 ().f) a f7 ~ j U22 == ()J1i lJ.t 22- 12 U;Z1 . ?)UJdJ nn:2()u C?..JtJ:JhdnoJD tI/.; JJJu wb.J a'l< (112, an I Q n Clzz a 23 i I Ujf a?;2 0-)) . ~ t75rPJ.1uJ2JnUJoJo 'JJ~aJbflf!:"(l 2JJrY.5(;J7fJ(!!'JoiJ(J; (;,2, '3) 1 {2d n 1 (3, 1,2) 1 (3, Z ,f ), J (2 , I, '3 ), (I.! 3) 2). Jn1J3Je.nn !.JJJ() mtlJ2.sbf} (!!1':J/J()J 1 Om{!!'1ll /uJ() jf) - 3JfJtfn 1 JJ(1tf!mJ JnnJJcn uJJ OJ;}hJ)C'u .J}6fGJ bn'JJOn 7J +- (( 1 3rnf!:'rn UJJiJ :sn - !Y>OJIYJ ») - (t. J Jh()dJC? aU 0- 1 2 an a 21 (J22 a 1 , = al1~iJ;3ta/'2a2?a~-t a r P2P32- Qr{l2fl31- a12a21a3;; aI1Q2J,{r)~ ~J f {l)2 a:r~r ~ sMJ3rr01J d9UJJJ hn2f)iJ C?.JiPJhdnOJEtfnt :JJdmm](!!'nfJ d.Jhtin3rJ b:JhCLBn· JbJb()J J. c· /.; J d !J 'Y (]] b iJ r?n 1J DJht.n @J !J J h ':J /; (} 1J bJnbn. /;.5Jj':JU7!J~'le()t 6Jnbn b:fJoJIf ':ill Je? JiJJ JJdmn:J':)/uJJ ~ (f t( ,1 -t ,) j.(). n + (( bn')!Jnm ':JDt'?S J](J(!l/T!{]l JmJ35n (!?n.52JmbJ{!!'tb.J J:;rnQ};f) .J{!!'.J{]JfJt.fJdJU Ld h J J C' (I ~ .5 n 2 mhn J!'m C'!."?1J!J(!? J /; J (j !J ::J ~ b:J Bnu !f' 3.Jh rn:i3 '!In (bm '!J() .J f!!' J 3.J5f!:iJri' 00 {h; 3C!:'i3n . nmJJt!!'01J 'jdJJ3n dmJ3Jhn tE'flJ2Jrn6Jf!!'flU ;jJhJ(!!,2~-'JhnJ, bm/!!'fll n -£( Dn'J6n(J) "jbf3J J3f1~rn(J) shJJ{f}JJJn tYnJorn5Jc1J.J JjmP3f7 .JC!'JJ:J6'lfj3n/; 6JdnJ3f!!1() f!JJ nJ m1n dtn(!!1t?liJf!JJ UJJj5(J7 bJfE n[ r .J.JhrrV3 'In Jj m!)(J .J(!!,.J::1J 5 tf.J afJ l £JdlJJ J C'.iOn 1 !7indJ(!!l f!) J PJ 'jd1JdJ J )U;; (1) J 5 J /l r. fPf)J 2JmOJC!'nL J JlvC'-.JC!'':JDnJ . L'JhjlJnu lJ.JIJ!J() ](!lamdJAJrrJIJ dJJ&.J2J2n; rE':J1RJAJn5J6'Jft .JJJ3rneJb ';)D t?J OfJ 3'1DJhmtf) Jflun3:J In!1)]/!!'f) {l1nn utfJAnimDr; (?J bJoAJ3(!!'Jon (JJJ3fJDn on'dbJOnCl 2;Jdm3(J]3S(!}1(T1(J) d.J!klJJn bijJ(7/.; Jn6Jr33D{!7 + + r?JtfJhJn6J5H'L .:J3t 'dJJ(!JJJn dnnn{f)JC"f) (J)3nlJJoJan: i) dJf1'nnU()/"; tfnJfJdmEnhJof)m ~JJ!.Jh3f7f)Jf)J:!J7 .Jh fI!J'J~JaJ' ((!h.JdrnS/JJ(J1 JL 073fJuJ6J JJmhJ tPJ JJ1JJJ'J nn;]nu f?JIJ'JhJnOJ[)!ljonu073n/.;) JJ 073nuJtJnrPJo JJJrnJrPnoJhJma J5n'dJf):](!"flJ3JDfI (gJUJ3D.J: (!YJtf:JhJrJD.fhdnl 5:JJ.JC!'J (J1?JnuJOJ , hmo.J(!!'nu UJJ.Jh07(!rJflJ[)rlJ U!Phn.JrnbJ6num]fI/; 1 1JJOJ!J(J}C!'(JJ!Yl n:JoJ/;J &3JlhdnU (J7JnuJLJ· JJm!rnJ fYJI),fh-l.J5n (J}3f1uf(jj{Jn u.J3d.5hnUnJ Jrn3n!fJ.£I77iJ1 d/Yn(!T'fTlC? iJffhn:imSi3nWi3rJ/.; 2) {f7':f (!J.Jff.JhJ()bJlJt!()L hrnJ.JC!!'nJJ utfJhnjmIJn 5':fenm3.5&JJ' <3J'JfJ{) .]{; f.!JJo'.JhJnOJot!n EJ'JC"nJ.J !.Pmc;nJ· Ju 07JnuJCJJ ':JdJSC!!;';'Jf? aJJmJ(!JnOJ!um[)u (JJJliJhJfJoJotfniJ a SDU.Jfk:?JJ.ionf!J.J5 . JJ!;(J)(!!'JL!, !JmJJC!' DJJJv3{!!'(jn dmOJOfl(!"JmOb Jhmn .J(!!7:JJJfitfn (JmLfJJ!JC!() S'C:'fn?JJ0n !JtP/v,JrnD()~dD' 5 J J NfrrlJ (J7() 07mJ 'J {!7Y1 J u OJ diu J C'n IJ':J(!!YJ b cf(l1{!tY)J CP J floJ (!J() J O'!f (!!'(If; 11 fI7{!" (1 () j 6' i3 J JJ(J)() '5J!J(J1f J. n· C!?JJfJIJJnlJJblfn· 7 3) 07::1 rP.JtP:Jf0n5Jo/fnu nmdX!"nd1 fJ!f!J()jmo/.; (3J35JAJJcnJa07 !unoJ !xlII/deL?) dJdJb C?JtfJ!Jj(}OJoJ!(J/f 3JdllJ~JaJ JJ hnJrh3~j· ~ J.5n(J)(!!'Ji! :Jrn3Jf!!' f)JJhJ]e(J(l dmifJ/J'.Jt.n hnflD3tbJ 2JdhJ](!'1(IJJdJ t1J()tJlrrJ (T}JoJ 0 JJJIlJ)C'() (!JJ Jdne((l) J 3 IlNfoJfJu (jJJIU3C'c:JJ J (f!()(J}(f)J:JC!() Jt DJJAJ3C"() [!JJ I !JJdJ- bJeJJ:J, 8J(fJ() .3JdnL!· 'i) (J)'J rY:JIf.J!JJ()6JIJJ1nu IJrnJJ(!TY)Jj mh lJlfh():!m5L 2JJ3':JifJ[!"(){1I J(!J3f)(!nJou, fYJ/fYi J()6JotPu dJJiI)c:!'Jd.J 8Dm(!T1(T)~ fif)'JJfi(). Ji.J (1)3n!JJ[)J s~3nc!nJe dtfjnLle.MJ (!?Jtf:;hJnbJbJf!()u oJf)UJ!br::3hJ(J(JbJ {!JJ OJ~J5JLoe.:i3nL r:JJJt!?JJf7 CiJ/)!JJ6nb jJ f9".Jd3Jf!lfbJ: (/)1) (JJeJbJlf3(!!'JdJ'Jn M J(!'1JOJf)IJ'L dJ3')[f]CfJ{)l JC!?,]nL'8L,. dJnfJJC'JJJ dJf!'.JbJD'JC!'.Jdnb f!!"C- iJf)!rnJf)JaJ· I)) 07') C!!Jl?Jld. JDJf)Jfi.J mh/J :i>mbJnhn !Jtfhn:Jrn&i Ji.Ju , !Ja() 5'J(!'7f':i; ffrncnnJ. c. 1 JMJ)C'J!I 7 (J)':J JJ Jh,mb.Jn!J ttlhrl:JrrJi:KJ& :3J?;<j1f3(!!'lJm )(?3fJ(!!1Jd[" £?JflJJJnbJf}l!() (jjf)!f3~Uv JfI1jrJ,~JJMJ hmybJfJ(}). (lJrrlVt J6h13 , ttlhn1mfiJdlL .JAm6JrYvnd()U dx?m , d()YlCJdtrJ fJ3rJ3J (?j ff.JIlJ() I)J !Jf! t. J/l OJJ(!JYJ(J)() MiYOJfJ .:in , W:J C'!Y1J.f (!JJ3()u !JfT1jlJ')(!lJi--/vf.; ~~m/; , JAil L ;; ':!{!!IfJ . CJ (lJ'::f @Jt!JhJnoJ!iflnu hm;lJ(!"IJJJ bt!))f1}mbnu !fm3:J~f) J(T7'JJJDyn f)JlidniY2J!)IJ(!!Y)J m/lfl ?JUJJ!uJ()[, "$Jonu W!:r7m , d.!JnD Ju {P..J#Jh(JflOJliJ!1n ':JrY!Jllu mhn @.J!f:iJ/3n5J!itfht 3,)010 , hmJc:".iJ'Jnc '::J3JC"J M3J b/flll1dmSn n2Jn3JJ, kif dmlf'..J(hC!!' tPJJf.JMn5Jbtf9f1 1 JeOn'Jb':Je:Y1 !JJPJydm0110 5JilJC'!'Je JIJ i()A 3J C' @J;jJj!J<3n5Ja!'Ct1 JMb Jfllli t!!'1l tJJ w jh:J2;,a()bJa£ 'J.Jf!l,]JS/Jr!!'fl /.; t!!Jf):f mOn , 3Jrnf..J (!J:J1f .Jk!J (l 5..J5tf'J(1 jn - ;}:Jrr-M 'dJwJ),JJfJn];JaJb ';htP;JJ!Jnt!!'n !.Jt#JfJjmfin . J.!J, . au . am Q 1+ a'i ... a/i.a ll LI ~ 1 L!J in .. ' ... a ..... {L Un1' .. ann n 1 n /l I J.sh:nC!!'J II, ;)mIYJd':Jcnn r:?JffJMnDJbl!nu d:JoJe3JD.Jcn .':!m3JC"" {11/.;JjA:i3u J:I?J& u.JOJ a, i ..( aL + a/~ )... Un -. C3hP,bflf!!'j3()U (JJb/;{/J0 '!!JJf:Ja ()a() JmeiJU LuOJ t oJ 1 i LJ i J" / II a ., {( - a . + (2 .'" a..... a - . . J .J, LJ' f}J IJ, lJ. f1J n L n L JnIUJ{!-"{J :?nlnu rc~LJ3Jvdj2JnL 1JJ2n !knJ3!l'JJiJ In!JJJ(!T' f!JjtfjAJnflJ[tf£ 7 oJrrf,:J rfnJ()b a'/;.)3 !YJ3](\nu 6..0n jn -fLrrrN C!!J}/JJI1Jm)J 5ffli· t) jj e J fP~,}dn;;J6 ffflL /vnd2(!!'fI]:J !J ffAnjrn5 L (?J 3'.JosjJj3m JJJ3J r? J lPJk!h[;..;bl!fl& L1[;3" 01f!J(1:.J n O ~ oJ8/u:c fd':Jc::L hJflc}j /Ylly6'l1::J, J(Jnm &nJf:iJ:!J(!!'f) {EJf!:/JJnWbilh ,)0 fJ.Jnjf.J(!!'.J oJ' .7!J (f):]nL:jeJJ :::::'J':JJC'(rl(!J JfV]~idJ ~:JlfJ:J!K3r£..J;;ff()L CJ- 6. /.17- J ~,)'?J-5 (J)jr:.. ~~~ a.JOn:" rEJ!.Jvf(J(!!' J o:J(!!,() 07Jb JnorP:J31Jrr2n ff) (JJ omj JoJdn07 . (;. ~JtfJhJJfiJEfn0 )(!'lJ;}JfJt!hf., dr£rnnn (PJ .f(!!lJJdJlJf!!'(l (!?JJSlPJJJ. @.JlbAJfJ/JJ!J1fflt 3Jd(!!lJ utfIYJ..1rr£.0J/;) r3J b3:;#J6rt/'; JmJ~3(J(}) r. - ':inn nn3nt rPJrfJhJniiJfYtlnL J<!T'JoJ6tPnt (] n Em h n J5'm(!/i3.J nJ (n - f) nn2;nt (!JJI!]A;}n /JJbtfL , hmoJ(!7'fll! d,'}()C'JdJ dmIlJJ'Jr!"() (!JJt.fJ.JhJnwfJt!n0a.5D) 0-;') OJu2!fJ 5JmJdC'()(J) nJ L,tfAn:/ ,;;~~. (!JJ D!.'1 tfU? hrnJJC':'Ofl(J nJ)rn f!JJ(;.J JrnifJ!J':Jr!"fJ :;;:;dJIJ 1!'n. a ij J (!n JJJf)!fnu dn&n1n uU ~ ; !JfJJJm(!!'mmn JCn.bndOJOJ· a ij .JC!"JJJlitfni Jr?"t3J6!e.(!!'() (!JJJJ!JJ;].J A ij -0n Jc:.non'Jcoa..: !Pi nCiJ dJ[)nUJgcy,JJJ ffmC!'mJn(J1: A Lj ·""": {-1)L+-JJ1;j . 0JJ.;!,(])(!!>{)JMJ (J) J m !J J (] J. (!JJifJhJrJiiJ5t() ':JrYhnL Jnw IJ.J6flLC)fl.J/)r; !JtfJ/;,dm&1u (f.jJtf()[) 3':": J j5 tfJan6 07Jjfl!JnJ.J J~j0' eJJ.5ffJ;]Je/61 wd.JvJr!:'tJJJ 5Jo!.J· J·fI . fA / = azfAift a i2 A z2 T" '-t- UinAin' ( d.J.fJmr;o)(J) JJ 07Jm!lJJnb UJdJAOJCnfJJbnJJ :}J/.;.)JJ hrJ3fib fP)tf:.Y-dn&JlitlhUJJJfl/J. 'lJ j S () ')3 [) J. J2 f!JJmf,JJn~JfJ {!JJ f)J (J)J()!.J..fJ()~J5, hrnJ mhfJ .JMOJffin IJiff,njmonb o,-!rrL [!JJfr.J!xJ()oJIJtPn o':JC"nL umf!!'()J 1 JJJmJ~()fiJAJrn3/'; (!JJ/;j?J/).J ~ r:? .Jlf:J!kJfJ[;jIJJfJnt hmJ.Jf!."M.J tt!;~ jmbr,u (UJ:Jtffl0) J(!'"'Ja.JlJ!P.JdfJiJ 1JoJJ ulfiYljmonL (!JJ.J!fh0) 'J.JbJd.Jodfi ]C!:"JJ.J[;ff:; dn~ .5(!!1JJ2N:'Je!' (!!JoJf!J«J(;fu IJJolu)f!!>{/JJ !5Jdfl /)'!J{!!'nL ffm(!!1f)J, J./I. {1. A· ~ a· LJ. +- + a· A. := 0 ( i t-J') . L1 J i J., 11J 2 ttJ J n & JlJ)iJJ(J) , A JnnL ()-'J!Jn hnonu j3Jr:?hJtf':J~ JJtfhntlf)· 8 JJtfM!J'U J5mCOJdJ A eJ";t! nr)f/()L 'Jf2JJ'J!i.2rJ(!!'f/ JJfPhnffn ,OJ') A· [] = E {5J.5 8-A = E. (Jan A- i Ur>Jom(!!1mmn Jc:riJlC6i: (J)Jrnf,J3nL RJJm!.JJJJ(!!v0i2JC!!'Jr!J (!J.fay5rJu!;J"J.J 3fTlf.JJ':JE'n 3Jtlhr7I!nL J,/{- J(]jJ3 dnh.i2~C!!'n 3J ffhntfnt t.r6JdJ· A JJtfhntmL 3MJ3dnhjJ':'J{!'Y) dJfflYufn A "t -Dm .J{!}flfifJ doJJv {!J.J d.JO n - fJ.!6f:YJJJJ '(JJJeJa5Jn/)Jr:?; A 3JiPllntffll- JmJJf:1J. .J(!'1]d:Jol!()t JrPan(!!'JU ':J6c:'J RJJ6JAm (J' Jn1Jn)j J~aJah':'Jc:'(l (!JJ3JtPiOJ ~J 3rn?JJbr!?nlJfT){]l (lnC!:JJ'j(!!'() JJtfftJDh~ JfIJJ5LJmlirJvJJ J J. f). Aj~ A 21 .- ·A n1 A f 2 An'" A h2 . .. . . . - - . (J) J m h J J JJ. !J m 3.1 (!!l Jtu (JJ(? J a?J sm 0':Jf!!' J J t1frvr!.J 2J J !if,J ?J.:BNJIi:iJ':X!!Yl (!' J () on (3 JJrnn (fl 3E'.J~ r:JmJiJ':Jf!!'MJ1 /1- -1 = _1_ . A't . /l IAJ A . (_1 A*) = E ~0 (_1 A~).J-:=C. ~.5Jtfj()rljaJ. J[)E'') (OJJ.Jd1P.:Jni/mm ~ 17mJ I ri I (Ai· mfvYjJ iJ1mem3J J!.Ja.J3iJJtp Jf!JjMe JJJ I JJntPrrJ 3Jt3.Jbrnm J}{1) -JNnn , ;;JaJC!YJmJ~, JnfJJ(!!'()' ,SJnwOIJfJiJ '8J3()u()J3(!!'(r)(]/ A· A ~ OJtfhr>1Yn. d.Jtfhm./'JdnL aJJ!J.J3C!!':k3nL DJ!.Jnu f7J.fOJDo';(!J, oJ3hJ?;(!!'(J 3.Jtfn()i/()[ Cij J(!"JJJ/Jtf() 17m3 J.fJm)c1J}.f{!!'m(f'l, A JJtfIYJl.fnL i..-'Jfy., /..;t!hfljrnhnt .J(!'"'Jc:;f){hO(l (11.11 a L2 ",,,, aili '1o@J JJJJJhJ]enrnrn A~ J<J!p!)()j.Jh[ j-'Jhr' LJJtfr.' oJUJa JJ()/.; J{!" JJJbtfj?/lJ J (!? J Jf)(!' f6':J (!'l(J fijJ/u J C!" iOn r;j.1 J -j IvlJ m OJ· dJ2hJJ, fffi,.J;]L JmSrf,;r}JI.J JJ 3m A:i< -niJ j -'J{j !JJj!f8(l n3jm'?3J6nJfi J(!!lJd.JfJf!JJ(3n: A j t ) A]2 ).. , J A jn · Jentfm2 Cij ::: air A jf + CLi2-Aj2+'" + ClLh,Ajn' "' J j J '!? J b-, (]}"J (J .JJm3IJ:JJI) ~aOJ t i:PfJtJ :fmllfOIJ L ,] n6~(!J 3 fJ (J) (P.J tf.:JIr3rJI)J!J !ffl L ?,.kJ en f] L b:J U J J 2/J) 073J JfJuoJO dJJmJcp()!JJIv C?.)!.Jj]bJU J JfiJ()t!5JOm, !lmJ Cij::: I AI 7 hm!fJ i::: j (l7 J C-- :~ 0 /lrnlfJ i +- j - Ju jfl ()OJU 6()'dOJ3l, IJrnJ A· A j;-- JJtflYlL/t jJrno()J WO] 7 L-J . lAIIAI ... O) ( o I IAI Ii . (_1 -X-) _ (1 1 0)- E 11 IAI A - 0"'1 -. h ':JIIfJmCJn.J6 In fJAl!J()J se3:it3kJe L3JblPfTlC!!'.i!JJ{f).j U()UIf.JJJU .JjJD U.Jb] aft X j T a lz X 2 +'·· + ()f~ xn:=-g i ~1 X 1 ~rl:z2 X2~'" +~n:rn= £2 ( i) -CLm1' X 1 +' elm'l ~ ~ -', - + Own X -= Em , n U.!r?JIJ-' at) J 8) (i::li:<,···,n j j:=1)2}"'}/)7) /JmIflJ'::frl!'n !7I7ifb3.J3rJJ, Xf~~)' - v} :l'r; jf uJdrUJJ C!'n ':)IYf)m3.Jon. (Jsb3no(){!!'m (J) JJ cP/JfJLI'.Jdn al~ {l12'" am O-zr CL:z2'" C0.n A= ,x= ami Umr' -U-mn A C/J!Phnliu Jbm(!J:;2;J (n bnLJcf.JJniJ dJJfhl"lIln, X -iJ uJdf1JJJf!'"'n JJi/MLffJ (L3J!f-!JJJ!h(l!ffl) 13 - L, j{) I.Jnl!fJ:JJn6 JJ/J tJJ6J dlvA-1' d,;iPhflff"J(3()L 2JJhJJcnJJnI, DJwtSJJ5 'J'd':JJC'(77 ('.J 3JJrnJt!?nbJlurnJiJ 7 /ynJ (1) bfJtffJJJ JJ1f/>rJ!J:Jf!'J~ 'Z!Jnd{!"fcu JLJ -fi.)()fJf,no[ /)2 '2J1d07b3J3Jd() ' IvnU'J A JhnlJ JhJlJ.Jt:'J33Jh:i3':Jf!"fJ .:'3.J(lJlutP:JC'"''J OJtPhfJu() , :',' JJ!?IJnLf:JC'!'n aJ51PmC!!'Jru (Jjndf!!JJ"JJ JuJ .JdrnnbUJ.JL ; A-i. (A·X)=A-i·B ==> (jf=A),X=A- 1 .B ~ E.X-A- i -[) =¢' X=-A-:i·B 3 jh.JdJhnL, 07JmhJJ.' dJ-JbJaJ 17- ':JifDm?JfJJD 17.- !:h'!3()3 a.Jfi!Pm&JJ.;(JJ.) LnLtPJdjL, J.().. oJ 'dJ(}07bJ.J3Ju., hmf.JJ-Ju.Jif !.Jnutl.Jr:JnfJ d.;IP/)(}!f'() ~3.J~tf':Yt!!'f)...J· unLtfJJn1.J JJtPhn!.J'(lU (!?JdJhdn!J.Jcf!'rl .Ll. -(JJn .}C-'36n'd5mtn C"J d.JU unl.JthJnL J(Jlf3.JIlf) r2JtP:Jh3nDJD!Pn 3,f)m~m (}). a e51J@J JdfluJ 1 J.§3flOn ~m[J) n - IJ'J(!!'f) :J. tr CP.J db/} J h :J fE.J&:JMnliJ[;JfJn ; Ll 1 1 ~2 ) _.. 7 D 11' hmJ(!!,J6n!J1 JJMUJ'b(!'!kJdrJJ!i JUJ: j -':Jl1n rP.x36 JJhJ ~jlPJAJnr;.Jr; f!J(l hm2 dn3()~,"(J) , bnttf:Jdfl/.; JmJ?JJh (p:J1P.JMnliJo1f8n j <;11('1 /;.)) tfnu ljlf3(!!'S~ ':JEJ(!!J fiJ3b:J!Ynm LnhtPJ3nlJ d.Jn1i3,:;bJ a!JJ}.J, J.f7. rl{l ., --B r .. a 1n az~ ... gl, ... a 2n D. J G.n~ ..- .g n -.. Un" (J) (J):J m h:J J &i. (l)") n JU'EJrr0nJb h C';'~n 3 JC!!'a:J2JrJC!!' (3joLPmf1!'.i2JJ{)).J !.In!.JJf.JIJ I1U dJlfhnLrfl JhJJJtP.M3Jh:iO~e'fl.), a,/lirIJ 1Jn1J!P:J3JLJ Z)jJ~linJ .JhtnJ(!?.Jhmn JdmWbL5n tPJ nan ;}mfllJ.J;}J ~mhJ:JC'!' JJn07 1\ .6 1 L1 2 'Y' _ Un Xi = D ., ~::.6 )... 7 ..A--h - F . I!'Ja1f!JnlfJoJ. 3nwho:J?J~rnt!l un1JtP:J3n1J dJ1PhnJ.rJC!!'() Jdmbtf){){!J- hmM>hlJ' 311LJflm X:= A-i. [J . .52 f?mC!'moniJ 1.J/J'JJC:JC){)07 d"dm3tJ73Jr!:'m07 Xj -'Jf!bm6(J. n2Jn nJJmC!3:;dJ X b3.J1fJ dJtPhnLY(1L j -'Jh UfMdmf}L.J t?J jnJJJ:Je" tJ.JJ.f'Jn· dnL J.:JnwOJ3c.-.Jr!")r? A -i JJ!fhnLfnl J-'Jnn L!J7Anj(f1on!J JC'JJJOffJiJn 'Joe.! ;P3 J J/J.J)C mC7 8 J;~fr1L jM3J{!"(J u3.Jffflb JC!'Jo.J6tffo£..J t?~ onc;fo:JC!'n bJJIJ.JJf.!'Jdrl (J:;3:!Jhr,{Jm07, (J)j dJ3nm3JC!!'/luin6':;d(1J) Ar> a A- j. = ~ . A ~ , dnJJ33nhJ(J')f!':'n osrPlY>LfnL dJIi/;.!beJ!JJdr;CEJO 2.MmJ(!JflOJIU ,23jj5..JaJ . x· = _I A . g + _1 A .B + . J-A .g = gjA 1 j+B:zA 2 j+···+gnA nj J [j ! J i L'I 1J2 b.. flJ tL 6 dJJhJd, 'JjSbJ!.JJ(ij(!!'{7 Dn(!!fJenL J/vJ/YD3.Jt!!'8n @'d.siJ Llj C!?JJba.JlJ.1 t5?:Jtf:JAJ()5.Jbt!(1U O.sO..J(JJ(:::'(] J(l/;(1 j-':Jhn L3:JtfJnb 3nIJ.1tE3{)(J} , jJf)1fJrnJ x· = £:'j (j=I,2)"-1nL J 6 J(J7jJJ{]J 1 ;J Jhnt m X!J hnJ(l0 JJflOJJ'JrnOm3JDn 3.s!PfvJLfn, blT1{!!'fn K (lLJ (J) () 5JtP:JhJt!.!'~~n 1J(Jf/'~~u /JmJ.Jf!!YJif j/J JCJdJiPjdJ In (OJ /} IJnfJ"6J:i2J[ 8rnhfJl ,J/.mNU 1 (j.fo]nbnC'm(Jl /J\ (J'.J!Phn!f(JL [)jdnLJnJhn K /fJC1{1 UJ!/Yljrnf)n (!7.J K jf.JC!n t3J!fn. o.fl)!JnbnC!'m., Jd :~hnjrnfiio(}UJ C?J !JJJ/fJ.Jn& OJi?J:)).JOJJfbJ d0'dmJn :J(!"JdJlitfJ(JnL,J3Jr; ;}:Jf"a.7oflC"n K .:'n?>nL :qJC"hJtf~C!:'n dJtP!Jnif(1- ,J J.;J:f!J(1fJ'nu (!J.J1P.JhdnO.JDJP& Jbm('(JdJ JmifJJ~<.:.nfJ A OJtflw!nu K -':Jhf1 hnQnu dnDmIvl. IJ'bJfPfJJ, K -:J/lfJ hn3nu dnf)rnhn A.xJC? ~ 5n3.JJ , brn(!!'{11 01') K -t 'JJ3lJ3e;[1tJ) 1-(!JJ5 min (m, h) -J~.J J d~.Jdf!) In,Jft!JJ~f!:'n dJ tff;r.!in L JJJC' JbJM 3fl6tnh~t. dJ 3f)n'J&nt7J ,hmd f(J:Jo l !lmh G:kJ{T) (J)dJobfJ (!P'':! ~ fl J~J().Jr;tJn0 o{)Drnfv1 n-':Jf.rJ AfldflL JJ1Phn!Y3f1 f).JhJmJ{!J3Jf)L (f)-f) /v0rll :;).,~-JAf!) 2norrJ1u . (JeIbuJ'be .3h.2dJ· 8.5tflYJtJ'flb h.JDon -:JbrntPJd.'J ntJ{f) Z W~Iw~/I hnLYo3t, ftnJJebJIJ Jj3t. ClJd(!?J2>n mhn (]I3ri.iJJ: I) .Jh.L.Xmdt Jrnu.Jd:JC!'f1 dJ1f!YJtJilf.- .JM1fJ clJfllitl tz hnJ nt !JXflWdJ6 3J6LJb3J3JO'!JC'() dn!Xnhn 1 2) 1. -f!JJ -:J'3!'1n dJf!}'sf!:YJ hnanu ~3J(!11 J In 5mhn 5 ':JC!!'flt tPm (!!'f1J J m j C1 .J r:' IJrnJ 3mJ 3J OJ, )j j /f/yJ1JJ n/.; !J.£jjfl J />r, & J;; dJ Jf hm! flu ;; ':J (!!'n bJ3.J 6' 2.5 r; LdJ 3d 'YJ 6'jC!!' dnornh[J)J lj!EIJlPJufl hn~n. A JJlf'hnffnLJ hJbJn Z (A) -OJn Jr::3!Jn(J[)rnOJ· (jrn~.JJ:'f(!!1I1J n ':JiYf)monJD .m 5'M3tJ3 d.JDiPmf!!1:kJJ(J}.J UfJutP:kJ.J (luX! -t (&/:z-X z +···+ a!/JXn-:::.Ei a,:z{ Xi + ~X2t ... + fl.zn Xt)= B 2 (1) 3m;}3Jff) A JJ LniJtP:Jdf)U dJiPhnIJ'nJ' 2JJr;3f)lJnC!'m(J} OJJPhnIj() , hm3:}{!:'fl!/ dfl()c:J3J A JJ tPAnLfdn OJ;' t3.JDJ JbhnfP.JD bn[1P:JMU 2JhJ3:;bJ ob.JlJfJ[2Jb (J:;tP3..:J!J/1{!!' fl u3.Jff{)U f!..JJJtP.Jan~- JJ dJiPhndiJ iJ()1JJhdfliJ aJ~.J;J/JJrni±1(!TI() dJ!P!Y7/fn 3~b""{llm{fl r.- c:'.J . A WJmC!!'m07n J<!}][;n'd5m{f1., j. n. (l,u (lIZ'" (Zin g f A ~/ an·· . {l2~ B 2 G.m1 tl",z ." {ltntv gm ffbJ~(jJ 1 Am J i (A 1 !: lZ [A) . UnLlP.JoJ!., Jr;m~.JaJ ())J3J.;20J~n ~ ~ 3JiJ .Jh07fl dJfJoif udmlJJ.lJi.Jofl .JJ3!J ) DnbJ..J c JC?:Jo CJ.Jo07b3J3Jdil - JlutnJ3WdJ@(}. UJ 3.Jn ()] e!' flJ 6nJ jAm bJ3.Jh - .;j.;}.Jf!!'f)!.J 'J.Jd~.]J/l tJ? .J m h J J .J. n ':111' b m MJ 6 In fiht8r> 3 J(!!' a:i3lt~j{!!' aJE tftn<!!':JdJ {J)J u niJ & :J<3 J (J)J 3LJ3J!2f1 J JJ'J1l5 rY.J Jbmc::'mr:;; JJdn61 NnLYJ JJ iJ()1JtfJ(j()J., JJiPNJiJ'nu hJEJan :J:Jmh3JJ.) In&n3 J JJ c:3JhmmJ3 'jC!!'n dJ !fn()!J'il0 hJba1.J J J- (). hmLfJ '?: (A) =: tz [in. r;j .J 5 () d ~ 5 J. IJl71/rJ t( A) .( i (/\ ) }. jnmf).J.iJh -iJ!Jt!!rJL mJrr-AJJJ d 3.J~.a 6J6,h IJmJ vfl!.JtP:J/lJU Jdrn6.J6U:;fJ JA J-j3l ,NnU'.J 'Z{A)-=-'![A) - UrliJfhJJ[' .Jdrn O.J 6 '-'lJn JiJ&, dJ{JhJd IlJd(!?:J/Jn ? Ju -:;/)(!?J dJrVd3.Ju '(J.J!J1PJ36.Jn/)cJ(!?: !f6J~J DJ ~Il las ~m f!> , 'Z (A) ~ n i (J):J i (A) =- f1. 1 JJ (jn5 !Jnu!fJJdJD .J!xnJ~ JhOYJ J Jrnb.J6L o() Ji]t, Dme.nfn (Jl"J tz [A) < n ) JJ 'Jn6 Uritf}jJIJ t3JJf.SfJJ '(jJ3hJ3n JJmoJ6LJ)n, 1\ nnllb3lll1JrJ JrkieJYltr0J. ~~f'hJb, h~ oJ5!Jfbc]/)nL JhJJ 6JJr.J!JSC!":JA /)(J{/DJ(J)J !.JnJ!UX!:'..J' ff3(!:'fi ./ f"J6nL Jf,J jn - bJ]C?3r,:!:" nr}fJfJ3!Ji) ~f)ahJ3t!roJ, hnd'b3fl(J}n dnJ(?J3hm3u JornC?J3.J. f (In(Jr:?JJ!JmJJ 7 IJrrJ(?'(Ij./ d&>'J3f)J{'!'mJ:.JaI1J a i :: ({nJ a 2 =f(2))"" a n 7:; ·Un))··· Jc:n6()'J6J6.J (U n a2)·-·,a n )·_,) JblJirYC!'Ji?' (an) unJdmC!:ifJ(J{). O-n.-!J)Cfrtg.Jd.J JnJ{?.J3hrrKJnL n-'Jnn JI) ~m 6 J c::n DJ?JM· rzJ j 3 mu.s~~ .3h~r!!'rrI3J. {a,v JnJ(pJ~JU ..Jbm('lJ6J 'd.JJrr0.lk'YLJC!!Yi £.J;; (T) r:?J[; (d3Jd~.sb) f (J)':J 3mMJaoJ~ 1lL](J)() Ai (m) Awb3n ., hrrd w3nUnJ/vi Il-{}(Y)[ f2n 5: Ju (an ~m)· ~J3NTdJt j~ d:kJ~, OtJ /1311 axJm~nJ f.rr0rrN.J wdtne>5 , n1JJ .i J:JJrrV:'.£ d m 5 m f! m5~~ 13 J. ran) JnJeEJmCJJt .JOmcpi3.:; Uc!?~(J (Jr!!'ilJ/!5J) jjjtN?Jffh .sJu!.0'J d5@f)) 1 OJ':) .!Jm3JC!'() fJ.--uzJrL O.-n .<CLn+1 (an>CLn.+-1 ,an>/an+-d] an :::::[lnti). ' rohC>Sc? ] .k"_'0J{:J] .:A/1J)~Y2 (!'J s))JjC"~ Jf'k1f!!JJ!>,id:J6IJ dmomlPmb'!JlYl Jr>3(!}.JYvra.J2r, J6m(iJ.JdJ' J (] 2 tIJ:J:!Jh mdfliJ 'k:.1JJhfJ. CL !¥Jfl'6:::L J~JJJ [~n 1 JnJtEJYvr2xJt bs./y) , ill'.) fif3fluJf1 In n (? .5 c?.J J n OJf) f hf){)'b:YJ1JJf.Jl3r\l.; .sNLi2Jrr:;)IJ n L.J [M bJ!f'dv f!!':YJ(I no !Yw-'6)n) fmC) / a().- a f <- £. IYnIlJ /t>n 0' nb ~sJtfh , hmJ [l AfUJ6?Y1 J!1nu ((2fl.) dnJrEJ3hrr.2nL, 0eJ.'k1 , JLJ l;~J: Jim an =u . fl--;CO (TtJ )n.J~J~ ajj~&-lJ ~j}{) J OJ!> jh:J6J®l :JEJfI'}(?)~.), CmC!"m SrlJ.JJc:Jf.!?J3 ';J:xJIh63J13J'dfl jf) '2JJ5'JCJ'JCEn. ()';JmhJJJ - (j)':) dndl'?.J3nffi3..J 31)JaJ~nJ J JJ(jiJf; n:afl dJJmUJScYoC"'n.J @JJfiJJnil.JdJ - ic.jJJ{]l) (fI..-...,; .Jf,J~';C?f) 2f1JeJJ~.J CPJ Jrlin SCJJhIU a, J3nLmOl DJOnZ;;fl.]/n C?JI:? jJ{)(J){) f hntr63f1 - ()JI0,JOJOu nL'l(Jl() no 6mO.Jnn J AmJ / an- (1) < £ ,hmilJ n) nO] <so'::! a - £ ,( fln -< 0.. + 'E ] iJmfY J I)) no, aJb3nbn~mm f).J3h:i3n ~ u.-i.. Q2 ,"', eln, Jd bJ3!JJaDJ «JJ CL- [ h(loiJ.JIJ ~u 'JdJfnrvUf) J JC'Jbnd6m01 m -nm ,6mc:Y7l Jd D.JYU{;W C"J a -j- f nnlJ'D.J0 C/rr/l()U :J&1I!2JUn- Jt -f)(J)' 3Mn!), Llb5C?{)J, JnJt!?JJ/'irr0r.u !:JJJC!!'J 6JYvi C?J5jJ.Dm~t!!':JJL ':Jrfl1r!:'t11aJL: m ~ at' :;:j{. Ju jf\ nJJIJ 5na6J_~L ,Am'] (an) JnJt:?J3nrrUJ ?/.JJmwU:YoCY1J 01JrrYVJJ C?JJtfJ.JnIJJo')C'flJ '2JDn'dJDJ- Jr.JiE13Am3nL o:JdrnuJf6c:3AjEmdJ Y>..J..! !JJjd..;/lrl!J11 In!/J j!l.J3.Jt?rrJl)L07JrL ,'JJc.J f'7'() m.J!!? ( I) - !) 1, - ! l' _.) :Jr0C:'J3I>rrilJ, Llb.Y!?n-J J d.JdmJ..u9::c:kJC!YU) dJ.6Iud .ifu.,J .:)/J:JdJf!Jf). oj w M X'rn f! d UYYU dt1&? J 3NrJ.s - ( eX. tJ) J rdl?J Y'-rrdJu .J:)1JkP .7oJ '::fwV\:] t:::'fT0? J t/r/l J JMC?_J'Yvn.2J J, [7';:J I jrJ7 Cl n :::: 0 , J-n· cO :;ml](l1l(J iY 5(1J6()(JJfl f hnli'6?fW~ dnr.dJJ6.i?:_' nL.J{f'/1 no fJm2JIJ (I ,hmJ Ie< n 1 n--co L 't. ., nmLIJ 17) 11 0 . ':JJhf)'d3IJJ, JnJrYJ~u ~ rYJ ';)!.l--.JJJh'::!t:!!'m@ dU'rIIJ:; dn.J&:JJ/lrrl2:tJL 3.S5wC6c~(!JD 'Jd::JJC'rnrg t3JJrr&?()f).Jf,Jrr2JiJ 1!Yn3 //m ~n :::. Cu J/JnS (?.J J/xn0"'mC? cJAJnfJ 1 IYntfJ anJr?~?;/lrr, a..J 1 C> !) --to 00 (~n-(I) 'YuJm':J(!"m{? JlIf'lVJ' ub3.JlJJrlJJ~']/.; nJJiJ &1d6..J.3iJrAmJ (L JfIJ/..; (an) dnJc:'.:J.3JxrJ()f., ~:!JJAn 'JJ'Jn5 ~J Jb1Jt!r.rn~ tlJa£, hmtf.J Ovn 6JIr!krv>~an5:k3.) UJD!){f): ~n=' {L+cXn, UJ(?.f if (d. h) ') wU/J~f(!!'(Tl<!? duNJJ drJ (!? J~J . OJJmh:J a.s. ':J!.JJf.}."Y(!!"(lkg JIiN0 dndC?J~J 3Jdfl ':J/;J~ JorYvJ. r:' J J t! j{) 11' J '0 J. J&:! 5 3J fz3J[ rn 01, f.mJ ro (eX. h) C? J (.r n) ':J DJ LN::'J(!!'f1)t!! OLfrY1J ~.J?Jvr0iYJJ , .2.f'dnO ~ =CX n + Yn dn2(JJ]30rrdJLY '!.J~ dLJh'1.JJ· 3S[;3n!J.n(!'VT)0I OJdNxJnJnn C?JC?.Jdnmn i MLYb3n. nJC?3Jb' :Jntvrd1(J), km ex n=O ,.klrVfIrJ ~) 0 r n4CO :< I / L / !J()JJ'!JXiJ.JaGrJu ifnrrd:iJ[;.Jdj fJ!/J (]).tJ h <J 6mdJnn, hmJ do n / <: 2: I 1vnL!.J !7 >() o. J£..senrnon 'j A J C? , II ce II..., iJf7JIl.d.J36.JdJ t1LJ01n no 6md:1M, hmJ I fin)'<' ZJ IvnffJ n )no. J(!13f)ncJ(;mm no-(}.{j) ~C?rIC?J Un n ~ -!.J.J e J n;' -!J 2m 1Y1&. ;;.J ';)"[)1 11NerLJ , hrnO 1Ynl/.J n) n t?' dJ 1J/J ':f tI"~JdJ rnIYI3J ~JJ m cndn.J 3J&J cr'n ':Jtf~J' (J/'j 3rJIJJf.a~.i2xJJ j)m~::J(!l'f1U Y107-:i'J(f)f1 m3tlLi!xwJ) Jn3t1c:J3ffJ I D n I == I eX fJ + )J n I ~ I d n I + I Dill ,( i + 1- =:. £. J elhn 2>.J ~, [;:16 nL:JniJSC? .Fe:'.J2t:x!:rrJ L:> u !>nub3flL.J tlt3f1lJ R 3:15 ~ rYJJ (Tf) no 6mJ.Jt¥J, hmJ IOn / <. E, !-vnJJJ n)no' .J!J j() nJJ!J onlJ5J':J...,.,f.m:3 (On) ':J!JJLJ\':jf!!YlVSJ dLiMJ. JnJ@:)~. mJm/u;).) C?JJrfjf7l1J(J':X!?flJ· (lJJmlJ:JdJ _ 2JJ~ J~ (!JJ ':'J1J.Jl.i\J(!!)"T1{!? JIYrlv Jrde.J~ 5JJAf30Y1 jUJ/JlJ C!!' rn {!? d IirJu 0 flJ (!:.J!;hrnoJJ. CPJJil:){)/YJ(JJ. ~oC?5 35RJJfmrn) hmJ [f}".J [(Ln) 2JJm!J./br!:YJ':!J(!lY1.) , (d n )3fJ- 'J~ a dfl!l J, J./Jnfi Y n == an' c( n ~m JJ[; LdlX!}3k1(!'YJ Jf'.Ck:>.J 3AtTili ~. i.:JlMf!!Y11~ a Lr'nAJ.J (OJ n ) --n!J 2JJrnU./}x: YJ ~L bJJm rtJAiJM j2J!J n (mJ1f1 A 70 h n!Yo YJ , Jvn J j r1- f1 J :s. A .'fn 3J Cf) n -m YJ ir 5 3n~rn(JJ 5f3nIJonJIJn C)D M11'63tJ. hJfPaJb (cJ. n ) "JWU/J"J~19 dLlnfLJ.J, JdmPtnJ ,; >o.!Yv'/;YJ!.J.Xh3rJL ;lmfldJ?JoJd.J ()LJJtJ)tJ no f)mdJM, Ilfnd /cJ. n / <. ;; ,hintlJ f) >no . JAJMi f /rnl c::: Ian.' ~n/ = Irlnl /d n / < A -A:= E,. J. fl- J f\, J .( [, I1rn Lr'J /)"/ () iJ j J.7(!l J5 :1.idmJ8JIJ .JvtrV3u 1 hind (0n.J 'J/u/)r::; (!:"fnc.) dLfNpj- 07Jm!JJd J (!J.x:J tP_VI ryfd'::J(!r'(lJ (JJ :J m h :J J J. '::)W LJ-.'J{!!Yr) (3 ;; LlrIu In 3ci?.J3hm "6 JOU wdA;}X!"(7 -:;11 JLlC/(Eyn (!J a!J"rllUJ ~ JJ l!3I1 dJa J. Jnb.Jl)(su5 ':J!J.;U-,J~ a Ifr-lu Jfl2~Yxr0J ~J, .3ILia~ an) l'PJ ~J j n 'JJ2mbJ~(!1?Jd(!!Y) 1 sJfl!Prrd j~ J1!'t'IV arJ~J~j 2.J3(J1~~J· .JJflU axJm J (Jl'J rrJ,n J /;J LN:Jc:' (r)(? J LfrVu 2nd!!? J ~ J!J J/lm ---:JAtr>/.; J J£3flbnf'!' J 3 (J) ~ 2lHflIU./bt:'3IJ"JeiJ, dJrrIo u j{") 11m a (rid]' :; u.J tl1:J ~ m@ d tI N0 iJ , r; n£; (fJ.Jrr/uJ fl!.J d J c:Y1 01 J J tJ7() [; JdA.;.J ev: n .J £.JJ.J j wUO <!:fIle? d U'rJv (JJJrr1v2 J (!? Jotf.J()/.fJd'J (!!{)j, "jj;JUv:J~I1~ ~ a~. (A n) JNe?JJ/JIr0JU J[;rnrEJ3J ~wf.;kJ{!!'(11t:? c:?fI(?(l. (JJ:J 5JQn0JnJnn JL>O !'t'u'b?xJiJ.Jd)};(',i JmndJ"JEJJ2JJ nLD07n no &n2.J!-YJ,nmJ IAn/)).0,hrndJ (1)/lo· Jd ~/vr./; bJNfJ -. lim A r1::: o:J . n -4 ()O f) J '3 Jd tJ?1/jJ ?J J (] n , /Jrrv( J (A (J) d nOt?) ))-..n;j J ')!J.J LkJ f!!' (/\~ @('(!?(Jj (!J J 8 (l!Jll KJ?0J"O () a))., j 3 ~ n 5tTVJ 1Y\C3 J Ii C? J 5:Jili en (!?.x: j2>rltJ)]drlJ bJl0~.J) C? j::£ -:;Am : ft"m An=- T oCJ {Iim!h---- (J::J) tJ ... o::J f)-rao ~Y1 dJ ~ (;:i3f"J , Iw-,;]. (A n I (A n :I: 0.) 3flJr?:1YJrrJ.J JwLkJ~ &kB1J J./Jn5 C? J J&n- C"fn(? !J./dnb, IYnIl'J (Ai. ) JnJeJJhrnJJ j!vJu ';]1JJu;-..~cm(J d uW\j. {1 ':JUJ£h':JeTl7U? JIfNrJ J/lck:J~m.f dj'9~:JOJ· {fJ'j (d n ) r:!?J (0n) j1JJ~ dfirAJ JnJC?J:Y\rr\3Jdw, JJono Cf],J JrJdt?.J3hrr0J dJnde'.JdJ njm0: ':Jf.JcJ/.;h'Ye"m~JtlmJJ~J~ ~JhJOJ' 3rJt:13J(JJ) (d n ) (?.J (rill ':)WUi:J{!!Yr;<3 J1J'r'JJ:JJnJ(p]3 !vn3JMJ- JJOm3Jo, hrnJ : J) (an) ~~Nn JJ~j(!TY1 m2f1G ':)LulkJerm~ JlJ1J/>.JJ' 3tl&JJ (J;n) , {J>'J 11m ~ n=.O } (5) ( d /1) C?J (0n) JIJ0l5JnhrJ MOil/..; ':)w!.kJ(!nrnfSJ JO'MJJMJ ,(JfJ Il'm ~ -::: a -FO ; n....,cC n~ 00 J on J ~n OJ (d. n ) (?J Crn) JJ3n3J(!".J6tf':fttJ J5'iJ lffn(!T'~UJ 'J!.J..JLh':'Jf!'VT'i!' 2u'N.J:00 , OJ'!) //m ;:n == 1 , {J-#O:J J-n (J).JmIJ:lJ.J. OJ'J (fLn! (?J (8n) JnJ(?JJ/-yrJ:i3tJ ..:5IJ~, dJdNJ jhJ258J ():/5:k3J (fLn+Bn) 2n.3C?.J3hrrJjJJ {?5 I/m ran+6n)-=- lim (In+lirnf3w n--1 co n400 !J~(}O ~J3tP!Jn[j.i2J. Jc;3(jn'JbmOl: !I'm an::: [t, J lim Bne:: B. 2J2n5 Cln -::: [1, Of n 1 g ,I::: g+ [)n' n~o::J n~oO !.JJEJ[j (cXn) ~J (!In) ':JUJukJC!'fT)(? JtlnAJ In.d~.JY>rrJ:J2flJ. 2J.J:JOJd.J an + g/1 = a+d n + B+ rn = (a+g)+ (C<n+ Yn) . JJ2:Ju-J f (d n t 0n) JnJCOJ 3'Yr20 ,1Vn2IT'IVf ':)w~ Jtm!JJ and~.J~ (f}J 5J3n) n JfJ:}3.J '-!J LuI...lt:X!"~ cJ!ioh..J ondc 7 .J?JvreJJ. JJ/ld}'n(}} an-:-On -:: f(l.+{j)+ (cln-+f>n) !f'mf!!Y'f'dlC?JO Jn3tJ(!'J6cnJ hrnJ ([In+tSn) 2ndC?:!3ArnO.) jAfcJe(JJ (!'J //m ({Ln+-B n ) -=:: u-+B· !J7 Jm'!)].JJ 1.!?0::'!,r,;.:J2:::::r.. r ,--...." (JJJm/11dJ. OJ':; Ian) COJ {6n} J!1d(!J~n JlLi6~J' dJ'dnEJ Yvd.JEn n-fo:XJJ (Un6/J' dn,]@JJ!vrdJL/ c='J lim (an -tJ/l)::= 11m an . limbn . n"-' cO n~()O ~oo C?.Idt:f:>ntJ':J6J, JC:~EJn'(J(ifTl(JI; Jim an-=a, limf3n=:!5· dJdn£ an= a+-d n ) Bne::B+ j\ , ~QO /}400 Wr.?.JLf (CX n) COJ (0n) 'JUJUJ'JC'!YT1@ Ju'rJJ7 J()JC7J3JlnlJ:J2xlJ :33.JJfiJtJ.J an. . gru = {(l t- c{tL) (g-t- f\vJ =: ~g + J J rv UJ(PJf/ en. = a[)n T gCXn+-Q n 0'". jU.JL),':J(!T'Jf)(? 8lf'M.J 3n<J[!JJ3Jvnd.. ){J)J (J)3WJ62Ot"JfSJJ5 a.JJ~,: ts n ") JI'tdr?J3r..mO J ndOJoJ :7wLJ!O(!7'mC? Ou'n/)1- .5dntfJmJ, flrJ-l3 n -= M+ Yn IPm(!T'rr0J{!JJ.O en J(J C' ]?J(JJ I f,mo (an 6n) Ji1dC?J?::/v7-JJ .Jh.JdJ(!?()J c?J //m (an -bn) ::= ~b . n --+ r:t:J (])J(lJAJcIJ C?JJ t/j(]ifJ(bC!"(Je' . OJ;] rnn J.3 J, (J)'J (an) LV} (g/1") 2n:}(?JyYr0:i?xJ .d1Jd.ff!?()J. JdJLOJ.J; I; m !!In -+ 0 J 2J0f1!J . n~oo ( a.(\ ) I' U-/l 11m a JliJ6 rC?n ()}IJ)JJ - In.kOJ:YYr-t3-J1i (?J !1m --:::= Il. n-<oo &n n--- cO En I;m B f)~..o n 3f)r;_r()~ J 6 t)n =-8'!-f\ 1 UJesLi (f~n) 'JiJ.;{;!J'J[!!'mfSJ dr./(J!lJJ, .JdtJlfrnJ i i _ i - 1 _ - S'J" : ( gn - -g- 8+.0n - 8 - (!3+0n) 8 1 ~n = ~ T (- ~ - B~rn ' fn). 11m _1_ - _1_ tfm~ (DJ!JJJt!.:YJff~Jt? IN-!JdJ)(]U1J 3A3.JfJm8J ,!vn;; (_ i-. _i~. G) n~ co b() 1) ./ g -8+ rIJ r n dndC'?.J 3/vr2; J ';)!.J J1.JJ j enm(? a LlrYU J - 3 nfl.J (){'!J .J /J (f\J 'tJ !J.JLkJ(!"t71 t:? d iIr/v.J' 2JJm'J./lJ!'?Itx!'() /; J (!J J ':'Jwuh':JC"mt!? JifnNJU 5.Jd)u~(l jn ':1L0U\::fc:rYnr:? JifMJJ' IJJ3d.ftY_:flJ 3.J'!;3:Jljr,o" hmJ ( 1. ~) 2f1&.-'JyYrJ.) d:Jdm!.J./!Jc YL/(!!Y)J _ B + jJ n /{5/ A jnhm6() (JJ B * 0 7 Jdfl!:J1md 2 -.:> 0 . liJt?e3.J1J (rn) ':J!JJ!.JkJ~ JlJ'rYill] .Jd'itfJrnJ tJ.Jhn:b(f) 5m<J/1tl@.J6 t:?J6:t..i2r!Je1"l 'd:;IA"](!"I!?JdJ ':JtPmr!:!'rr0J 11\1 <. I~/. ,JfJnfJl OJ::J ;)(luJhJJdf!:'.iJ(JJ J-rn (!?:J.<::' n u :f, (JJ - JA tTl n q) 3f1i.DM dI , a J..J d 5 j(j .J -B 1 /b-t?nJ:>/JBI-lrtJ/-.:>/g/- I:: I~/, Z sVtYJO' / {> i 0 I L.. _£ , !..JJ{){?.fb.J1f C'?J.3JU:B6nm 1 AmJ '(.p i (J, ) dnJ<:>.J3hrrJJ 'Jl{}m!.JJflx:.'Yr!C(lJ. o -to J - n I [;/ ' Df Vn J JhtJ2J J t:.:J 1 Ii m -ri- =- ~ tPrn~.) {!J J.JtP:YiI.!':16':'fCYlJ. JD(!!, J I rJCJ dJJm3rU.J1i:i3m lnyrJdL/.; WJ).;3 ~ 00 On 6. (!!Y)l 9:x!; Y1 fl l o:J {;J b .JCJ 1 d n YJc:' .:i3oJ . / - an j-! if)' /.' i /- i 1tfJ),D.- n 1m £2= 1m (!In-I;;; c:/imfln- ImB=/lmUn'Q=r.--: tl fI~oO Un {""H,o "n~= lHoo n!)->oo un 11m n ()--.> co 07.J m!u J .J (!? Jd tf!:YJ f/.J 2J::J f!!Y) J . J In YO 3.) [Jmen r:! .Jd tP j()If:idJ L a.J1dJ.J mhn ovrrJudJ ':J tfmer'trJ.:it271 tte.3.JhfbJ 2,.f.:!}~L::! !!:Yll,; 2.1 b..;D.J6 ; (JJ J mh:J J.J, (J7 'Y ( a-n) C? J (b/)) 2nd t!? .J3/lmJf"6 f1 dJ.2, Jr:PfJ .J t? J d.Jh:B..J::J f!!71 {) m3/YleJlJ (!1.J.5J-) J)[!"n CL n ~ 8n ,.J.f'J.,iJ Fm CL n ~ lim Bn .. /J--#OO ~oo (JJ ..J mh :J;; J, OT':J ((1.fJ) ~ J (Dn) jh..:8Jl::n dl13C? ~ , .5 j 3 iJ) tf-1nf!'Yl tb ~.':rUOn J /:>in f!"f'l ( (; !J ) cJn2t!?:J3hn)dJ (]LJiJ7fJJ 1 lund dJ!dl]':JC"n &ndAnf?Jo(5).J!D.ibc:'''(1 a-n ~ en :f:/3n, O..Jdnh (en) Jrv3C?J~d .5A]O~J !OJ dJLff /J3fJ3.] Sc.-J-00 !:J'j!..-, ,.'J,;~~ (' (2/)) -/.; t?-' (-fl. n ) -u r17Jr1YJJr]J (3Jml{;JLlffhJ!.Jf))· m'J onJtm3hmtw flm6rrJtPtl"/J'!IW (!J.J ';;JJmIJ..!k?JtJ(!t>f) ~ 3JJrJ /l.3fl Yi.Yx;er,,;. (T!JJtI:Yitf2Jj. (J.J!)!/0f!CYlJ/JI 3)~ riJ WJmD3J3.J, hmo'J /)fTl1YJd'::X!!(J (an) J~J3Nr0J ~J0'.JJ.x97j ~j tbJ J m& 55 :J.JJm!JJ Sc 3/J'2C!!'fJ. fl JJm<'?JD fLJJmLJJ!/.i!: YuC':'rn2Jnu JJJm nJf-L 7CJJ6f., flLJmn J1 mflo3fJ , Am {} jm3x!."n n-{l)YJ!J an 5:)J,. LrbJf!l()-) 1 J!.J.J(JJ(] j,[ !>fltrbJI1 ~jd-JJ(U.. fJJm 'Jrr0n!J 'YJ1JlAJU1 ,j~a 5mm 1[0 -nD1 (drfJni./C?:JdJ 1 !lind .)UJiJJfJ ':JJIJ'rJJ.Ju(J J!J!..JJ3mJ!.J). 3j~3.:J61YlOl1 Nnd /.;6~ Jl Jiu hnu6Jn ().15:JJJ (an) drKk?JYvrdr0 f1:x!:.J.>!Jfl' J J;;3 nbn(I'YrJ(Jl Ii J2ri.Jdn]/) n f) 0 IYIIfb y,. JLo - nL '::Jd ff MJ~ ::3 J Jm Jio - f !YlLrb2:l1/...:/ld flL, nJAfJJdJ3u ({If)) dn3C9:JJhm2JI1U fJ!J.J{hfJ S.JY>rJ (Arnd{[T1{)/" 5rndJIYur Jr!!..3M3&n{l) flo~Il(J)) , hmJ Un 0 ) ).[0 - £ - )(rdJJ(J) , n) /1 O' JnJ{!JJ3NnOnlJ J!...JJf!!'JJJC?rn;]f,U ;;J.d,r-n an) ana . Jon lfm d CL n -.:> Jf.. 0 - S· J:JrrVlJu dh!vJ?J a 3dmlC?J ,Amo an ~ Ji.o· dflcn':JdJtf.Ju an z Jio-t £ - ,)JIvJ a J C9,' hrnu'J n)n o 1 C/Jo3ndf':"f),) c9J36.J/un(JJ1JvnJ Jio-'i<fln-<.Jfot-£ ,';;;':1 lan-JLo/zf. )f1JC?J3!JrnJnu (Df!} 3hnu JJ5bj'lc'YvdilL W t?J:xJ.J:;enZJ {2.J JJJ!d3M(J),!vr0 /f'fh (l n .:: Ji <) . fl-> o:J nJ DJ2tnb3J3Jdn, /)rnflJ ~.JYJm1J MJ~tS~J~J ~J .:/JJLJff,tpJ<5 'J~Ll/b(!'3JJ'!J0Y1 Nm J IlJOJ JJfJj()tJ(;?:JJJ j~~sC?, JJ0YJJfP ':J&?J 2J!J3tlbn(!n(IJrf) JiJ3P:J~ .i3Jdnt?.Jo 'dJl+no wfb:: YlJ) m jy}fibJ.iJ!J 'JrrhJb :J~iJIJ f.ruJ6?J11 m 0 <:9J 3);3.J&nOJ ,Nn!J lim ail ~ /7} 0 f)4(J::J 5J] JIJ flU 11Mb)/}· i3.sr;~ dnO(!J/lYvndJ an ={I+ ~ t (!JJ ~.J3J<JrP.Y!ljm(J), Ima (}df) !JJJ3S81J' JJf)wmJ/)u 2 J£3r&Je."KJt1'1 JYvtnJ:) JnJ~f!)yndJ g n .:: (p. ~ t+-. 1 3fif) J fI (!J.5 f) i -/; an ~ 1 + r' B , LID .5C'?flJ, (fln )-/liJ j!JJJJ8f'rl2>nL rP.JWdcf.3()!t'.i3e!'.fl5J WjJJhtJLru 3sk32b(TJ{!I rv n (B -nfJ Jh ~ J@mJ J. ( B h ) (PSt? JM [J1 !'HI fJ'6 3m J 8rd?J Y-,n}J.JJ , .JJNfJrn/J ndfJ :f 3Jd 17J<P.£ a0n f) ) lrJ r;;c3/J';J(!!YlJ . dJc!J!JJrPJdJ] 3.Jtd0!Jt!M.x1/.; t!JJ~ {f)J!JJIXlJf!J, w~ 3J!(3:XJ(7Jm (6/))-(10 .YIJ~h~Jt?rraJ. Jdnw0731Ju ~!J t3~Dft1OJ j!lmr!'YrJJ (1f- X ) !} ~ 1-t- 17 . X (X:> - j ) n t. J{) , hmd.Je:nntr & h5'Je!Yl1; 'j ~ !J.J.bX"6~tJUJ Ld;m.?ilet1 (!'>J Nna:x!'YJ1J' JJNfh ~ au.:}(j1J' t?:J ;; .; dJmJd.J#IlXfnf) !I&P!:ddf/llu J.JtnI11tSh:JJ (tPJdJfJ3I1u'.i3J IlDrJ(!fl.JdJ :f3:JdtnOl)' L3JJd3t LBf)-f _ f£)n n _( i)n n (1 )n n j n bn -(n 2 -1 -n+1- J~t?_i 'n+l >J+- n2 "n+1){1+/)'n 2 )-{)+{=:1; WIl~JEiJI1' ~J3:J(!T'm307, AmJ (bn) ;}(lJ(!JJYvrJJ JhJ~/x:!JJ~J. \ (fl.n) dflJt?JJArr2JnL £C':'JY¥l e -tTVl JC!YlfJrJ'J[;.. i2u f:'.J d.J!J 5:Jl:JMJ hf){YoYJ .7brnc?.:J3J- ), () e= Jim (1+~ r /)-1OCJ I" Jrf~J6J, hmJ e M.JLT~ !>fJLroYJJ @.5 JvnJ e ~ 2, :;115" 'o:J1J5':1~ j tfnI~ ~.,J ~ - h ma' J f) =} r ':Jtftn ~ LJ'N(!J;1J' (!JJ3 '::IJ3J OJ, hmJ ':J ~ LJ.J JJ 11m (!"'J)j Ii fl.J h - tlJYJ!., [OJ 3.J;; J:JEm 01 hind d.J 8nb fI In !J) 3';;' [J)0Yl./YJ f):JS.:k3.J ( n +1) - (J)3riJJ ff, ;.,r), 1 JJf{3..JS/TJ(J) 7 hmd (/+:xJ/}-tf"/'f+(f)+f)X' 235:13L' , {f-t-X){)+f=(itXf'({-f:;:t~ (f-t-I):r)(.!+x) = f+ (17+/J:;:'J../lx. 2 ~/ f +- (0+-/] X j !ftn(!"m2;.J (? 531f.JfJ LJ'~.)- VY':'Jb:N(lfl.1J ~(!'JJhfl. sJ3mOJb,hmJ A J/)nL, ")=I'(x) OJ":16:flJ'M!.- !JJ(!'jJnn /)mllJ x---a (!'J O]h~C lim f (x)= A) 111':1 3J5u../bC!'YJnl, J!1n{; a -(350 6J[;L/;]J3JO'jC'" oJhe'nl!"f!U Q -j){i YiJOJfJn SJonL{!0 x .. G. ]hn (Xn) JflJ(!J]fin(;nUJ0J3nL (f(Xn)) In:J(?J3fIn'3.J j!J7JX<:YlJ A -jJo. n?/:;(!"'nw(JJCJJ' hiT'.J Jd 2JDlJ.J9:x:'YLJ2.;'(}n {L i?J ,~ 'J.JtJdcnJ]J /)':J~5J5 )Jfn,yTYI(!' !Jf)!J'03JdJ )(10) [r,,'Crr. f!hmJ6n: - DO,+-CO, co' (J)'), {l @J ,J, JAnJ6 h/)v!;3.J0(1, .5N.J d£](!"n (.'OJIJ.JdtPY1Lf:i3:J{!n(1, hmd //m ICx):::: A du(Jn5 ,-Cu .x~ Q }M}(!nmi!J dJj);)5, IJmu''; OJdnI.XJf1Y'lfI ,--OJr?.J6/)0Y1 'E IJnlJ'bY>Lvm3nu JhLJ&N:,/.; nlJ(J}() co.JC?JJf)iJ)(), 5 A~t0)l, hmd / +(X.)- AJ I. f. hrn(;') 0 </ x - a/ <.5 1 flJ(!1J6hf)3f) ~ia(l. JJ2tr0..n.), ~J A .JMi \) = {{Xl 5'JokfYI[ c.:JvfbJ£J ( JJ1lJ.3J5.:..) 'tc3j,f) a o~Jhtf'nC!!''{jn C?J oYlJf5 11m f(X).::A C J/m f(x)=A), (JfJ aJ5LJ./OC)!YJt 'yJ]{Jf) a-I J.:Jvyt/YJ"j x-;D..- :r~a~ (J5!J~3bn3) J~J3y,J r;y,!fJnC!'[J)j a- }:J5 j!U6J[!>f) SJonf.,;]ftJlJn (r n) dnJPJYJn0nWo!}nt (J(X< \ JnJ!'?J3NnIJ,) j!1JCJ<:?r.J A -JJO. 16 a 5Jhrf([(!T'dn [(:X) OJ':£Jt!'ooL (lJlvrb:J!iJ t?J J.Jh1f}JD.J 'beY'l.,J() .Jenon'JoJ2m6 , 'JJ!JJdXJriJ.J(p J -r ( 0- -) (!J J -r( J +) un J6m(!J'm:iJn 07 J rP 3n(!!'n 'J J D.xJ1,5 J YJ J 1 !JmJ /).J.()J.J I) y, JfJ()(!'" dfl c:Y:Jf)j bfuL ahNJ f1J ~ ~J yIy] J.Jdnf) C? J J Om(!YYTJ CJ J.J ';]t£, IYntlJ J(} 5'Jhtft]~() OJU d.J.JRsfl.) JJlwbJbJ (P) J.Jh6JJ5J g('1 J,h2,,1 (?J fJUl!if) ~0'::!"f/J .YYuf). {l]Jl1JhJJJ· otJ Jhu2:rrJJ6 lim !(X) (OJ lim grx)] J/2f16 o.Y>uJ3J<::.u 11m (f(X)+!d(x)) ~ ::c"'a X-.>CL X~Q lim (f(X)-f-/J{:x)) = JIm f(x)+-lim J(x) X--+ G. x--- a X----CL rJJJmhJJJ. !Jt:J JALJ2xn2JJ6 lim r (x) ~J lim fl{x), J.J2rt6 flJMJ3i3L II-rn (Iex)- J (x)) c:'0 X--+Q.. X-.>Q. r...,a lim (rex)· J (-X) ) =- lirn f ('x J- krn J ('x) Z-.>~ x...,~ x~a (JJ~mIJJJJ. (/)'J JhLJ6tn2u6 hrn f{xJ ~J lim !J(x) , .;J;LtJJ..;6 limJ('X):t-01JJ'dnb ~ Jim {-CX) X-.>-Q. X-.>{L X-->Q.. x..; a d(X) lim f(x) _ !~~ I(x) x~a J(x) - lim j{X)' X~l'L m2rnh:JJJ. 07':1 Jhf,Jdn0J5 Jim rex) tE.5 Jim JtJ:) c:'J a·t lutJoJ JfI(!J.JJm'CJn Lf")~(!'i3J j~- xva.. :t.--+Q. 6J f (x) ~ 2{:xJ, J./JM lim f{x) ~ km J (X). J:::---->Q. .r~fl (J1.JmhJJJ - orJ J,!)!J}0n-0:J1J IJ-m [(X) (?.J lifT] j{x) ? ni.Jn5f1 /!f7JC00fl .JfrlJ6-] Dm(!'Yn Ii (x) flf,XM x ... Q. )C->-(1 P( (, 0 OJ'J{)jrif)JJ, fynJ a-IJ hJno] J()(pJ/Jrn{]() 'J.JM'5(!"Jd':J(!'Y}.J 'Jt!rn{!"rr0J T x) :: li[X)::- a(V, dJ2flb nJ/1UaJdlJ J,3!LJcn31 11m !:(X.) (PJ lifT) -Rrx)::: 11m f[x)-= km {}t:rJ. x-· fl_ x~fL X-.fl_ T-ft]. _'/33C'J J!J [JJJmhJdJ ~7Jnc0"".J?JJ C?.k3rfYuJ'C?Ju ]nClDJ()hn 3!bnm, l.uD](!"errnn) <j['f:'J 3JJrn3nj]Om01 ';:'-J[ j u'1lnf., SC;)h()!J 'bJJmrMrnjJJD()C'(J' oJb!LJf6~ Y>:k3.J <?J ur0!?YYlfrbnL Sf!' jAn/., 'J J!.,JoJ3 (}]uct6JJnUJ li)xn!.::-<JJ RJ10 J5~JJr;!TliJ7 JhiJ7-JhUiD) JJJJ[!TY}(JU('?, :lr;uX!'Y7 . .sollWm3fJiJ Jr:'J6fl25JT1.1li: Jim ftJ:.)-::A 1 lim &0:)=8 X---Q. .x~a (7: oJo3nc::/!"tnrJ1 3~·5/.;Jrt[!}Jh~:' ';,':!J£ a -J..t£ J.Ji!JbJJJml!" 5.:h2\~0u-;.J 1- i:n5 j;JJdJt5YJ eJ6flL(lfl..!'"'i1 (X fl ) JndC3JJhmaJ' 1!3')5-j1J11nf., £C31-vV.J oJ5lJflJ{!'Yd2x1L dJcI"MJ lim f(:rn)~ A @J Jir() Jj {X n )::: S· !J ~ co fl--> ce dn3!? 13nrr'0n u .2 JJnL IfJ f} ?1YJL '3J!.JJQi3 rfl]rn.t) 'JJtJiJ 07 JD.;bJ J CP lim (f (X n ) T !JCX/I)) = ft"m f{Xn)+ lim J t:cn), /]'-'00 /r4co n--.oo l·n· Jim (f(Xn)+j{Xn)) = A+-8· c:J'JfrliJiYJL fbcJhr{, 3JOUJroC:YJJonfJ rJiJOJ!::dJt? j() jD M.JU En2w?:0. fJ~c<J ' h()l J lim (+{X)1-,9{x'J) -= A+B - An/; (!JJd!fJjn!.lJ6JLi cnnoC?rncoJ- X~O- ':J iJ J !J h 'J C!" m (3 J II M j ilJ J 5 j if()J. }( X) r::n fjj lr'tJ.J /; J f) i/i(!J j (y J 'J lJ J U-o c:!' m i5' J if /1 n J !Jmu' J :i -t- a 1 C1:J ]i rn n.:r) -= O· ':J W Vi':) (!'Yr'r!? J wli'J f1J ':J r; jutlJ a L a,) J f?, []ru OJ nu J (J)fl J J fll.>tY, ih3tJ , hmarnhnu I 'jw!/- '::J X-l(l c:: (T1i!? JLimJ Jnd!?] 3IYrlJ:BL, jJJ~: f) JUJL1l':JC!!'m C? JLlMJ OJ~!ij ifnJ(J),J 3JJ/1 jY:!"JJ ':JL..JL/oC/rJ C' (]Lln;':J J J 2; '3.J2mw fbc: };!lJ{!'YI OJ ':J bj lJ1)f)L;.) co J '-) JJUl "k" m (0 /3 fin!)) CJ ':)[; j tJfY) [, OJ diu 3eYl 'J[, J V. ':X!'Yn (!J J drA:J J, 3) J wU1':JC!" me? a iffY)) f!Y:Jo -j JJ f\.)(fL) 5.J3'w ~ '"f1 n(!'l J 3 ':J UJLN:J (!T'fT'iY J /J'nILJ J ':J W Uf, OJ (!'"'m (? a u)(\,f, 'J 03') oj U'fLJ (11.) 2J 3 J!..t?.:i2J,) , f)L.J YJ Ivn.i>rrAtJ d ~.J Yvr0tJ b g jJ mb 3 DJ dn WJ, ;)msr?JJDL 2JJb'::l6c::YJJf?'rrd.JiJ - JJIJ 33C"J?J .!L fubnu aJ[;':J$C'~ J.d3riJ o 11 "!fWIJ,'Jf!."t1/(!J dllt1hJ PJ"J5:fIlIJ.Jt1l.J hl13n ~J t!111~J lJft3J' 301:13J07} Frx) [OJ 9(2) U:;UJf/,'J eY"m@ JL%J "Jj[jjlifl:ffw J hrnliJ X --'>0--- ! f(J:.J-u Jt'mcpi].) 'J'Jnm JJcJ<!!YInnt/>& ':J.!J.JUO(!rr1l~ JlfhIJ11 3tJ@JJ 2(x-J'!JlnffJ X-7a,(II'J Jim C1J~D· I-7fl :F~) fer) (JJ :i{X) )Om&J"J.> JhOJ~ /}n2>nu 'JiJJLil':J(!J1(1)(f? J~ 1 NnIlJ x-? aJ OYJ I/rn -f(:r) =A:1:0. X~ JUJ f()j ~J 3(:rJ JbmtJJ3v IfrnMJU1 ':J!..J.JUJ'J(r:rr)0! JunA.Ji3f1' hrnlJ'J X-Hl/J OJ") lim f.CX) = -i . X~C- Jex) j A .1 j rf nJ j(!'1 J(,:, 1/3()nJ0! JrnLJJb y.b.iJX!!YJ J Lf'rnen '!3 J iJ 'JLuLil ':J (!7lm (!J d!.IMJ 07 J dJLJub J(; 'J Jo f5J J 3 (J :J.J h tf'n3 rl (!? .J}jC!' j &11J a .kJm:JJEJ ia J ~ m':J OJJ f).)J J J h J JC!'L 'J J J if.3 (!7'() 07 J n!J7 !:Pm f!:n f!JJ!JnoJ 1 <1 G? niJI JmdJJ~(!!'(J tteJ.Yl/l In '(Jj(1[,V3(!:r'.iJJ' ~ju', (JI:J -!tX) (!Jj gex) ~J!YJ ':JWU1:)c:rolnc? J 1IM:J:iJ/J J 1 hrnl!J x ~ (1 ) 'JJa 3/kk:/1J fP J 3 Ii .J/lln (J) lim (tCx}RC:JJ) =Iirn (:((x)), G(x){;CX) 1= lim [(x) ./im{Jrx)R{x))::= lim 14{xJ-!?&J). :r.~CL x-.;>ti d X d ') J:--nl-(] (;c) X-?Q. X-i'c.. ld ~tr0.5 b~'Jn. !fTJ ~&1LJhJu .J5~ ':J5'j3.Jtfn a [;:;htfht!:n3n 1 tn'J a e5'JhtH1(!"dn .5MJ2m?:JJ dnIYJ fbr::JJlJn (!JJ OM ~ ~dJ7nlJ dM23fj~J!.J JJ S:/Jt:fhe£Jfl ,J.(). lim /0:.) =t(a). X-+O 07':.1 f (a-) =- I((j) J dJdn5 !(XJ t?2Jt.:1fJJ!yfJj[ .JKfMJ:Jd,J .d.5.:..y~J£ ':Jb!J3:J!ffJ rl t::fttf(v:CrJ) bin C!:" m 07':1 j ((1 +] := r( OJ, Jj 2f1!j f [x) '!3 ':JD :flil1.J U .J!Jm tE.i3.J :l.JM3£nt? J;; '.J5jjJ tfn {2 g:JAJfh c'Jn. ~fj!JJ_1tPm2J.J Wh.J3(!!1.J6J· ,fc73rr1O.1/J, htnrJ :?;'j'!i:ftt'nJ ~5...H7J:PnJ fUfl<7.7 IYl,N.3(!}1.:1bJ, flL'J {)r]f1 ':J fJ'.YJ:J fPfl J J3!Xl3lJ!f!!ln L YnJJ (1T' IJ'Jl rflrurn '2n . 7J .d 5() 'J J Ii J. [a; g] !J J 3d J D Jf10 'J 'J 5:f tiM!J ~ IDJ:J Ef'rr0.J tbJ c:!' iliu:Y1l..uU (J a Jf!'YU:ij.i3J ) !vn:i OJ'J6Jdl1J <jfJjJ.JJ!n,) JJ uJ33JotPniJ .:im3:J(!!l dnaJ ~tPn{!!''Jn 1 d.Jhu-'Of>n@Jf) ':J!JJJJtfhJ B OJnJfJn(!r1 r;]n (?) dJ!Jf]35nC?Jo 'J!J:;JJtfr)J 0. f).JhEfrJen'Jn· , 5' JJ.JIff)1.J 6:ilfft'e'tnJ 1JJhJi2fJ. [J7':J hJnlJ f]jIJo-!l(!!f"dn '!Y:Jf)JtJJ7J.YJ .Yn!J '2w3JtflJ J !1/dfl5 J d b.J!J&nC!!'U J6mr:?Jd.J Jl77riJJ~(!"() !J':JIJddflf]U f]jJJ!f'niJ [;:jJ)fh~. (l bJhtfn(!"!J Jom@JOJ Nx) ':3~fijtl(){)u Jlfo<!"J2J.Jt9n r;~ 5Jlllff)(!T'fl J [JrJ JJ DJ!Jlfn(!"on JMiYn zYJ5 '?YJ5jtlnf!1J c.;ilrlbJo.; ~J OJh!/JJDv C!J(!'3AJan J fJ!.Jn()n ffmC!"oo Jhrufj, 3J2Jud Jh J2tJl63J?>rlJ5 -f(T) r::J 'j[) :J iJn nJ., ;;[) rrd J 5 J(!" rri2J.Ji: a fi J/Jt!()'(:!n'JrJ 1 J. n. ;(0.-)= !(at-) +- f{a). a bJhtP()C!"!.J _7!Jm!SJ:J6<J Jcx) flJ'1S311nfl!.J JnhJ2 {!7'n 23~/.; [;Y!DtPfJlJ oJ/J!fJ7(!!YJ 1 rJG J c 5Jhtf{)e-{]n JlJUfJrr0J5 r:JjfijiJf)nL d:Jl1/oJ5J (!JJ Jjh~3:J£J SC::JiJJJn J dJ3!lJ) (]UnD(1 tJm;'[n Jh Jhruo 1 :). () . f ({l-) +: f (0-+) . .1 ~ i ...u I / -V Q l~ (J) :J m h:;;; J. ':J fJ'Y33 1P '9':Jl) j ll'rU tJJ j ~Jiifl, 5.Jdlu 3(In(l ~t0 3J tPrJ S~ /..tfLJ.) 1 Drn(!rm tJI':J J 6nr;} 3[; J(!", n 255M 3 JJ j2t:JC!!'fJJ 5 ~ lJ.BJ5 , 3) 'dnJj 'J/J:J 3J tfhJ '2J:J'?J.5N? J d.J II· e? J.d t:f j n if:J "6 oJ. om :JJJIj(J C!"n iP .J Q:Jt!" .:i3r1 t LJ.Jd J A OJOJJDmJ..J 'j 2~ J un (!> ~ :kL c:J ':JIJ;1 LltVJ1J Y;~ 'iJ tfrr0n!..J (j5Ei!J/k:J/)j"J~Jf) (!1J ~'Do1I1Nl/..; 1663Mu (J)3nUJQ:i3ncPJb' CJJ/l07f!"Jd, OJ2.5c:nnOJJ ~ , 'j[;:; 3 J l? c:3 'J[;j t! (J.J {f1j ~ JriJ.JOJ3rIiJ a 3Jj lJ:M J: Jim (f (x) -t-j(;x)) = J/m f{x) + lim J ex) = f (a) 1- J {aJ· x~~ X~Q x~~ J.f A!Pfl 3.f c:? J If jIJ If ~ .JdJ J ;}j)J (J) 3 J (J)JrW1.J JJ -:;5" J 3 J tP t?3 ':J!J j Uf) tf 01.J h ITtJ(!"Y) ~ ':J r; j rJ n nt ')6:; JJ tP rn2> n !.J (}.J!..J J6.fa; ':J r; j J:J !Jl ~ ':Jr;!ili flJ (J) J h (J) ~ C!!' n '!3':) 6 j if ()J J O/J:J tJ) 3..J '6 C:13:1 tfh OJ':Jfjj Iit1J J. {J j 1!.Y.1 'j t" 11 ~ J 6:J Lfrvl1.J 'J J !JJI:,fJ j(J J lPJ ilLY (?.Jd J ~ hind !..JJ J Jh {lJ f!rVlJ &u '2 Jd (? :Jan {f):Jmn.JJ J. dJ'J '?Y:Y5j!.J'f)j c:;5'.'fJ.JtJ'ru lulldJ u.JL3JJ5JJ1D (!JJ O.ffJ :JJJfiMJ 'EjjU.J.J':X!T'n) d.J df1 5 {J:J;j if .J 'Y (!!' 11 "Y:J 5 j 1J'T1 J ':JS:iJ.) tf'n.J tJJJ 3rJ!.J d.fb u./b f!l YvlL .fn:; fJrJ . JJR3:J5J~f1)5n '"!3'J5:fllnJ _ f{x) = aX ((l>O , a,::pi, XcRJ °3'~5jJ.ftJJ ~5JJJt!hJ (/)JYV./) 2!Jou.il)(!!3h1l0 JAnu EJ-oN.JJnJll XD EJMnf!!'2Jn ;J.(J. Jim tl..:X =- 0... xo. J3nlJ (?JJtf~nlfJor.!.J X-+Xv !Mfb6nm on6.Ju/f'Jn 3j~3:;fJmtfJ, hind lima,x=l en ::r:~ 0 5JIJ ,-l,j!J·'CYY){)f!"mm d.l:1rnh3J.3j 1 hrnfl.J 0-)1, /;')j,7.JI>fJ1Jfl') .';J,Jf'JJ,hrrvn) /Jm:J lim (J x:: j e/J,) ·1' J:-)() I Ii rn a· -= i . :/rYl).Jen dmt"rr0llu @JWJt:P.YltJ'.i3C!!'j(...J 0 JJnUJru/)n 'L / () IJ()U'!dflu..JoJ.jn!) cU/') :-'f! X4-0-("" () ~ .!:JncnmOl nni.l63n 0= wJa..Ci+f)· LlbX!?()J1 'f))O r:?J IxntYeJ D<.x<o JdJdn6 'J:JuwC!:'{!Jjo.; 0jfrfr,em,J..; (LX/.. ft-~, <.--'5':1 l{l X-if <: t· Ju jrJ M.Ju IJr,'JSI3L -; NnJ )/m a X=:.i. (}.Jm;~ - x~o ... !:Pm 0'tr'J.J CbM (!" J 6.J 3n?Jnr:: m 01 ~fIYY) (f? J5, {/} ':J 2J:J2m3n f!:l :Jam -t. -= - X .5 C' fJ() CJ3[j J U . 0 fJ n fj lim Q x= lim (l-t = lim ~::: i .= _1 = i. X~- i~O-f. -t...,o... o..,t /"m at 1 t->Ot /JJ 3..JJtJJiJ3J3J(]n, llf7ltrJ O<LL<d. 5t:'3f)11'{J!Jrnm g= ~. I/b.s(?nJ gJ{ (OJ rJlJ a.J~ 1 ~ 3n.'JJ5i307 ~j3.J (PJJ!:PJnti'Jd':JfI!' f).;[;l1{!T'iJ, J3J.i5.JaJ ' x J. iii / f m a .= 1m ----x. .= -.--j: = --1-::: i. X--.>O X~O tJ Ilm£ X-+o ~JnOl (;) iJ~m~,J ~JJtP.3()JfJa:Jt:'nJ. J(l1./J JJdtniJf)i2YJOJ Of))(JC:J"J{f) a Xo I · fiX I' (aXoaX-~) /. !l X-Xo ",x o /?x o ,m l)...- = ,m . ==' 1m ()....- .= U .j..:: v... . X~L X~L X4~ l!..i1fT1ZJjhnOl3-:J~1l '!3'J5j{j()J' jrX)= I1ja. x (a/o, a.t-i I X/D) o.J':J5:JdN 'J[):;lJtff1J rfuYiU 3.J5 U.J ror:' _~iJ J/JJ{J() ,llmJrrYl!.f JJt3JOJoe.nru5f1 OJ':J02L!IlI1U dJJ1IJ'j(!fYJ t?J'15Jl'-'n,J· !JJI; n/;bflJ 3.5 5 n~"61i1IlJ. DJ!v0btn3J!;n fT)':}[)jI/I1J 5Jtf'JhJenY>11 J.Jt3.JOYJf.'.:"() OJ: ! (x,) = ::: X n (X (; R 1 nt j() 3'J5J /!IlJ ":!r;:;?;J/fJIJJ dmJcnIJ OJ.J3nu dJ {)UJtb(!'3M/.; JAJ(J() !JrnJfT'IJlJl Y =. X U J b f) 0 J D::J 3 j tP f9 'J 5 j Ii f)J (J)J r; .)J}..y?JC!'YJ , lYnf!"m D.5!vlU:m J J r; f) 0J'-:J5j tIfl J OJ 2 (!J 3fJ (!TIn 2.FKJ JI) J (j 't) C'1nm: ftx..) = xci, ( X) 0) d t R) JahJfJl3J '2ojJJtfh<J 07JJfJU dJ5f;J~{!,3!vJu JhJdfJ JiJ d.-JJrJ (On/iJ!urr\2V !1m 'Je:'fl 9'JSjlffYlu X)JJt1hidnlJ 'J-Jw6ia (J)Jm!uonC:>Jb) /)J63Jf; r =: a q lbJa.,'L . ff'hn2Jm61TJ3.Jff!J(J~ "!r!!&I1f'ti!xJ, J) Jrx) = Sin X ' J/; Cj':J!ij!JhJ 'gf):j3:JlfnJ !i:k3nWfJ Jh :r 0 DJntJ1nr!ri3n. :).(1· lim sin X -:::: sin To· .sJ()!J {!JJ!JJJtf!j()flxev(!> 6nOJbC.JA 3~~ X-<J.o A A (T)'J 'JJJrYJ3w3eh AmJ j'-J[JJfJnu IyCPI).Jf)'Jc-nn fbmJnu Un{Pn(O] ]h(f)ncn;n!JJo ;;n~ bnA9JJ MuJ d.JW2J,;dflUl fdx!"nu L){I2JIlJn/..; tPrn{!7'nJ, OnYlC'J6OJ I 5 in :t 1 = A8 ~ A c ~ IA[I =/ 'X) . JJ 'Jtfm~~jfJ, nan/.; OJ07JJf!'Y1u5'n5Jonm, IimJ / UJ 5 xl ~ 1' JJJji]J6u . ./ / . x-:x.:, )':.+-:;:(0 I 2/' x-J:::oj / :[-I-L:,/ I S/nX-s/nL -= 2stn- 2 -. c..os- 2 -, = sln-~ 'j(j)!J-r-/':: ~ 2 !sin X;xo I ~ z I X;xoj = jX-L/. JJhn2!Je? 1 dJ3?Jn.d(!'Y)J CPJ3t'JNnOl, fvnJ o ~J5inx-s;nXoI ~/X-Xo/' JJ t:Jtf1n(!Tl(r2ddfJ C(;(1JJf/oJ a~J/.;Y!:V1(J) In)n{!1f2J(}] , !vrJ lim /S/nx-sin TQ/=O- Jj.J(!JJ5 jn) X-'>X o [J) .On/.; J oM?J, a JJ rrJ (T?() fufJrrJL ~ J WJ !P,jfJIf.JMDl ItnC!TJJ' 6) J ('L) = Co 5 x· Jnfjj()~:1J CoS x= Sin ( .;-X), O1Jrnh2JflC?JD /ior;(!TlI) oy:;[jj!/fY)0 ':'10::;3-, rfrrJI10 'CJ!..JJbJ6 CP.f3JujJ!)()01, NnJ C!J5 X <:J~lJjd{Jjif ~f]:JJJ!fhJ [;.i3n/..;J(Jj/) 5Yl1f}(J(}71!J(). 2J) ! IT) := -[j x· /).5{Y OJ r; {j X =: ~~ n: (!JJ sin X CoS X 13':J fi j f/rJ:J2xJ ':J 5:J 3:1lfJ!Xl J!J (lJ 6 : J .J InJ1!m J a Jmn '2 Jf!3 Jh::? _"6 J ':J /J) 3.J J!f) f).1 !J:i3cJ !:f 3Jc:r' J 5:JA1PrJ(!!"lkJ 1 U.5t? J If j() {f) 5 :x -;:. 0, ]. n !13J(!!l.5 6.JAtPnf!!' d(j J 8J~J f+JlK (K f '2) !..JJbnU fJ:Jh!Pn[!7"J~J . .J/..; b.J!l/Pre.J2YJ . .5f.. ~ tj x - niJ ·;)JS/.;.JCDc?/vJ/; .Y1J'Jf) - Jo(}. }rX) = 1.:J X ~1J'(}J ':J5)J:JtfJ()J C2.JX'Jl/J 3.551JJ'6~Ynu JI--/10 5 J3nuJrUh fS:jJlfhen3n.· (3 ) J (X) = uti x - J u '!bf0 [J'f]J (j '!Jbj3JJ!hJ (JJ.J3n1Jn JJ5LdlJ C Yv1!J ,)/v1L; r; f6nudl)/) b:i1ihc 'In· J.(). :J3J(!}12Jo, 8J/](jJJ IiK (K t:2) bJ6nL DJJltPnc. n .i3n/';J· :J:dtf:fle!1(J 1fnfJdmfmJ.J~ '!!b5t1fJhi3n· }{'XJ= a'z.csin x (-I::: T ;:./) ) -!(x) = = flUC()s X {-{ ~ X~ () , j(TJ~ llu.tdX (XER) , !rX)=ma;f.:} x. (X e R) . .7!J oy.y;j/YnJlxJ, nm3rr1vr ':J5.'JJJeP ':3<:J5j//'!lJflU 9JjD',Y:'J(!,Y] OJ<:'J5!1fJ'!lJOn, ':JoJ3.JLfSn oJ /) () .J IJ- C}j 3rJ ,) SO] a Jl; !J.J S ~ Y'YJ/.; .JA:J fa 'd f1 , t;PJU j 3D,)' JJJc:r'J dnNJ(]J.J(?fJ JI2".JdJ!iJP..;A':J(!T1(l ~.1tYnJ ':J5'J3:Jtf'n.J OJJ Q n !J a J 5 I.JJtx:.' YviIJ .!k/Jn. OJ6(]'lJ?J5J. 2C"Jd:J5tfJ!l'X:YJ JOf!10JfJ.J (}u.1lJ7 '?3':J5J!Jh.J!..J 1 IYnJJ0YtLl dJIPa:;6() C!' n J C r1YJ (J) J r.?r'1 Jcn J JJIJ 1P jf, -:J f!'{1 ':!; ~ d If (J) df'J.J..J [p J Jf, IMiJ.J tfr)j ':J (I}Yl rrJ :YJJ LJ'f1.J 3rl/.; /.; J ~ Je""JOn(J). JoJ3Jefl OJ'JojfjfJX;n1J {lJ)n&fJ.fo(lCJJIJ {!JJ dn)3JO(][!"'(J IYJujY)()(!lJO (~cl':J I .5cnrn(5J J 5drr0f5JfJ OJ !Urn Ou , hmd bJMfJJnJl,n J[!'1 JJJotfJ!l'YEYl ~3':J5j ffnJtJ J5.'J~t?nJ OlJYJ!.. dJ6LU9Jr:' Jhnf...; ,'>!dJf1' rom (yf)J!J(lJ() d6n'J3£1'.!!'mJ.JE/I 00 3J!lfl ( i) Jim Siox::1. JJ tfmC!!YT6(J[, tPJWJl':wnd~J<:? bflWiJ{Jh 3~3.J&n!T1, Am;} lmu'J O<X-L~ X-10 X" 2fJn5 Sin 1:. ~ X.:: tgx· Jd :J~r/; JJhO'I1£J 6.Jbflf!!YJ t3.1&1J3fl!J :Jj1J Lf~, 3JR3JoM J.ftJ; 3JbJ SJbl'l!!Yl. J}1flW01YJt <JJ3Jr:?JNn(f) OAC wJIJrrAf\Lu (!JJ OJ) C f.;jJjJ{j)tJJC:f1!.: qjJf,()lrrJj?J(): .:.. i- j j S OAC = T ~2X:: ~x 1 SLiOZJC i oc·a = 2 tj T) cPJ ilJc?aJfj S OAC !. SO.t:lC 1 fJn3i1C':'.i6(JJ,!Yn3 X<. V:::G . (!JJd tfy,r!J3'1eY1 'j~J (jJJ WCYl~ J!/) RJ ?JOY1(1}01 WSX z sinx <. i. X C!J5X-!Y.J ~!Jrr0I1LJ lPJ Sinx-fl& jJbtPm3nlJ d.s~f1(J'il .x3J3fl(?TYJ 2:JWJf?/.iJ3fU1 hnJ JiJ ~J(!!'n ~~J u.x]Jf,(JJ(!!'{lJ/JI1J dJ 'lJfl!iJD', AIJll!J - ~ <. x < D. (Jl~ 3tribC" ~ ~~ J3.X!"aJ 9x:03:JJ f6J, lvnu'J T.-+O, J3JJ.;(J)Jfj 1 2J3rJtJJJJC!!YlUbf'l!):Jm ] NnO {))SX o.Y:J5j[/Ni Cj6J?J:Jl1m2;nu 2JJdm 11m CD 5 X::: tbS 0-= d, In.3I1(!' jj(J} ,IYnJ lim sin x .J.AW2xndiJ i2J 1-nLt !fmC!!YlJ' .t.~o X..-yo X 2) I;m {1+i)x=e. R3JO J]Jf!.3J5f2Jn ?;}jm5t:J.JJ hmc h(1]lfJ ncJ{,o./JnE lim (1+1f X-H't) X n~C() n JhLJ?Jm~ ~J JL 9:x:.>JJJ,n Jc:'J5/l'J6JD7 [-(]In. JtPjnlJ'(?J'2JJ) hmc3 AmlJ'J X ~ 00 5Jdl1iJ(]J/)JC:h dJ 'dn5JU' jim (j + i ) x == e . J(!, 3n en '2J!J..JJ-J:5J3fiJ, lYnJ JiJ Sf:' J.J/vl 'JjnJC":J(j-J fun5:J!ynt 'd.1JryJ a- X-Ioo { OJrJ-,Jt:?J l/: lim (1+1.) ~ :: e. T~O 3) lim /OJ(1Jf t X)· i ,wt:JJl/ En JcErJ'J5J3/.; C!!'rn2JwnJ/.; e ~ _' !?nx=~ T. .r~o X rna (Je J!J i(iJ:!I':::' .5<:' 3ne.'\;"@ Jrll'C:;'3 ~ E. "SJ }:£ jl!'],~ 2f1c::f?r:x!:.n r!h(!",-r0r1J..'£ gJc.. x CXJE:i:;;-;/..; ')5.13) & i,1(; ;,~ c.smJJC'f1[;5n5JJnm, &/l(Jl(!!'JIJ: fOr. ( ) i .l. () 1 lil71 . ,-J~ ./I~=.lim 'C>1 (11.'c):}: ~ .. I:)f1 !.Jim (It.'tr r } ~ f()1 r.-; )-- i x .r) ~L .x:-~o <. (L Go.. ;(:"0 . "fl.. kJ Je C0 fna.. x...." 0 x ') /' (LX_ j "1 1m _ En a· JJ !:Pm(!"rr0Jflu t?Jdtf.Y'Jtf.MJ dJM(!":MJ OnbJ J!1merrJrJ; d~iJ L--- 0 X oJ 3nm. .5 J n1J.J /Jl..J{1 L, JC 35n'Jbrn(}1: -!-. = a 'X._ i (5'J dJJon'J6rnm, Am;; a x ~6jl!(',f1t ':JD5':J-J!?rTJnt 202m t -f- 0, NnlfJ x~o. JJ'OntJ, CJ3Jj5Jdv n X _ j lim L{, ::: lim 1_ _ 1_=£1/ Q. J:~O X t~o Jim E,Ja.{ff-t) i i~o t -En a. hmLlJ t1 = e ] Jf':ib~Cl ';ynJ lim e'Z i :f.. X40 X CPJIJ ~3[jJ' Sin x , -En (u-x) , eX-l ~J X tfm(!"'3JU) ,:!f..,.;~ J/ffYui3l"J:;. NnlJ'J x~o. en (f-rX) ::.1. /irn .i b.)h3mXoC'nLJ O'Ei:J?0· 3a03Jm, 'Y= f(X) '!3'j5:Jo'l1:' OJbldb23h'.:lEflJ .xo S:Jhdh~I1L i\)na:J dn<r~~ ~~?J6n 'J6mrJl: 112:::::X-Xo. Ll~=Llfcro)=.f(xJ-f(Xo)' J:..r :Jbm@:JO,) .)h3~()J6t9()L~ bm~ l1')-G - ~~fijo'f)f)L s./b h~n Xo b.~h~nQ!'al'. 0Y.J5jo'nnG b,) h2 m j 21 'oJ ~ n h.)o2J f)jMn(!!1~() .:JDffi(!?:J6J ')d b:JhD'()Q:\~ ~'jQjahnL 5J~)enL ,)/)2/:0::16 tl'niJ 5)bht9ffi...,!:i 'dJu1>Yle.:0nL ~::.hL, hmd.l ~O'.J2.J5tl'11l> 5}t,hfPf1 JnnLb'hYCYi> 5"jC"'flL~J5 X o b~htl'f1C'3n "y=f(X) O?t'Jf:):J(J'I1()~ Nh;JmJff.JC"f) Je'f)Dnt!5JoJ fl(:Xo), et:ftr 0) , "')' JO ~ Ln:J6mC~I)\aHI. J. n· ax dx fl(1:o)=: lim A"J = lim -.ttO-f(T o }. ~:X:40,61: x..,> X 0 X-Xo cn~ 2J35n'J5J3<]"h hilld I=J:o+t,'J::, b.lhClrn:JQ'jC"nlJ o')DLdbC'~ 'dJndQ.".:;6:,.iJJ R)nbJhmL -f'(x )::: lim .f(:ro~·Kr)-f(:x:o) . o .6.'X~o 63:. :J1J D'mC!'m6') u..'>'J::J..'>i'!')6.ll> 2> 3xhn:J3L E)...,h£lmmC'n ~.y?>5'Jhrncn X DJMfll'!'31lJ" jJhdmc:? 11JLJ .'Jh3':13J6t1'r1L s../bh C!? LX 6Jhtl'n~3{1 J3Q!'.l?J LiT-nm :>~5n~5.)3m, 2l3Jd6JdJ j'Csc)= lim .f(x+AX)-f(J::} Kr~Q .6. X Gl::J "!>'J6J6'f)jj h.)n.3J 5:Jh6'f)~2n &,)-I1&1J !3.Jh2mWc-n, .'>dilIl"l2d6, hm() n21n .'>J b.JhBnQ."21n Ylf\L By" J"rti)~(\ Jb ~ \?n':JJh:JOu'MJ~n. (J):J '?:!>~6jdf),) bjhlJrn:Jc,J(9f)':' h,::,o{]J un2hJ.3enL ~m)JQn 'DJMf1C!!'dn, .::,J'DmoJ5 J hrr. J n2>() b.)ham i:3J C?n,) )3 l.Jnuru2!C!!'fhJ. 6j~2nhn ':JbDJ~m6,)uaub . LuLJ.1loI(!"ft£n.'> ~~2Il ffiJrnh JJJ (h~ ~~D::lO'I\) 6,)h()mil~J h'::'n2~ DJh~nC!:"dn, J:fEo5 f1C,(1 :Jro.3J!fmj).l jJ 5Jh~n.::':'~n· l':?::JtS'~flIfJ6j. 3<hd3Jffi, ':J::: JCX) '0~ojo'n:, b.lham~..'> Xc bYltSr>e~ '::I&9j 3.)-R3J[)m0>, hmJ dJ'd()b 0 I',m fCXj = fc.:cc} . ~5n4dEm(J) x-...:x:o feX) - f er o ) _ f '(4) =::- 0( ex). x-x o 8:,hJm~nG 2l.'>dm, IJ'b)(9;lj, fi m c< LX) =00 d./2lnO, 00 'aJ:'lbn'JW30"h hrnJ x.'-"X o fCX)-f(:t 01 == (c< b::) + :f I(Xo JXX-Xo j 0 "J d'm('."ffioM0 CbI!'3_\hfb'J O)<'.'.\L:'J~n(h, hmlYJ X"'Xo, J3Jj(jJa.:" hn1:J lim (:fCtJ- Hx-o}) "'0. J:!JC5'J5 :)0 ?>C:J2I~C'rr3oJ l?.l~.JJlf:)(1 (;'J():JQ.n tllT'e'moJLJ 0 x.., X 0 'dJDn'd~5J. :Jd mJmhJ2nG 'dJ2N~Di)~t'."'f) CQmt'."'J2J:, .lW:' LJili~0Ji)n. 2.lho'1C'J[J', .lC'?31'0'f1 'dJlu3rn&1i1JC"f1J' r,md I o "" 0 b.Jnen~'.3n f (X) =1 XI 0!>'J6!Jo'r.J 'JD:J3JcJ'nj, <3:'011.)3 :,h...,) b)hllm'J6:,19f) 0 bJr,2mJ3~t"oG (lJrnaJtS'hl¥::l~n Jq,hn 2~amJ.lhJm6L ~:JJl9:J3M: :f.('}:) ':j'j6:1um!.J 5.ihlJm:f.\':!C"f\ :r D b:JhD'o('."'2Jn ~L'?I,n/.; 0' d "J '3':J[)iumL 2>h..\~n~nU .MoLXo·, tlTo}} bjhen~~n 7.>.xU~:c(\ Joj),nL 'f')irJ.r;}, jl11:) "30u'n:J5BLJ. J.n. K::: t' CXo). JJnmt!' Jd, h,)i!?21J) .M c bJh6'n~'a(\ 6J,d.l).)c:"f\ 2b5o(\::,hriJ El"S:J 1 hrrJJen (J' (Jon {tro) ~6.) .Mo.Nt 2:BJmnl.tJD.'l5, hmo'J QhJ~n/bJ 2(l:?Jo.:>hJ }/", S Jht?oC!'f\ 3MLIJiu c:JnL JrlI) 5Jht3nc:'nlJjJb, Jon. hrndJ lIX--rO, cUdn!), ubJ@n,), ilrrd lim \J =. ex X «}J 1JX-nu 'jo.':J3JtJ>mQnu ;:jj3m 3?JjdoJo,) .6..X~ K' =: ti d. :::. -til (I i m 0) :::. lim t~ \7 =: lim b -f ex 0) := f' (T 0) 0 .1r-to .1'r-Xl ~-rO Ll ~ b'JhJmJ?t.Je:'nLJ '::)nlbnj:Jhn J<t>hn ~orrJJllJm6L 'ch3lPJ2J8n: /"bJ'je'nL Jmdh.llY'6o[, lJilRdJiD 'JC!?hn!J 3Jb3e'(\cf1 z,~L OY1 J01J2l':Je'U C?hm(\(J). j.n. OJ':1 S(t.! .x:bn'dbJ~[; GbJ'jC'nL Jruh @hmnL i 2md::l5tfo/"J/J\2JoiJ aJb3~ aCbJL, V (1:-).lJ j n Df)-R ::!..lh:JD 1:. 2m.3Jr) ci''dn, .d.:J'dnb V Ct:) :::. 51 L 1::). J..)hm~:,u', c£!lIn0L [i', -I:. +- L:JJ 'J':JJCC':J~8(\ 3.:J.o.3QC·()cn cLwn C!' n ndb"J60 SCt+Lit)-SCU, .jOnrfmd,JJ ~j.l~Jt98n LbJ~~L u:,';)jJe'(Y) unf\J.lhJ n:JEiJd,J SCit6iJ-SCt). db.)enJ~ nmJ Dot. h~u' '::J~m 2u'nhJj <?nm0LJ.1-1:. ~'::J..IC:'Jen~ Lj(JfJ~ LJ(1~jJhJ ~nm ~"::hm ,)bc:.mG ndlJjOJ 1: 2rndJS3'[Jn UnR:1JfLJl17u6.j.n Vet)::: lim VU.l'd" =Iim S(Hb-t.j-SGJ =: SI(t.J. t,t-tQ A 1:.-+0 Ai: / oJf)Jh(JmJ"MJ dnhrm,)(l?() b~LJon iY.JmhJLb. (J)'j fc~t) ~:I ~(T) <:'J'J5j(J'nJ6n b..)hdm'J6.:l~bn .Y1llJ5 X 5'~hBnC!"'d(1, cl.l'dn5 Jd 6.Jhl5'o~';J.') 5.Jl.arni3Jen ()dbJd.) d'\(J)(\ !i.)3nO' e:?J (fex)t-gcr")Y= :f'(3:J+9 ' (x). 19.xJt?j"o'J6,j .JQl~'d/)(no) : Pc.::'cJ:::::f (x.) + .9b:). a:'lJd~J2)J 1:>'(2:) -::: Ii m q>(~T~) --P(x) = Ii m (.f(x -tA~)-+- ~ (X+l(X')) - ( f (x)+:J (a:)) _ .4X~O 1I~ A~-}O b ~ ;:; lim HX+A~)- fCx) + lim j(x+Ll~XJ-~(X) -::: ;'CX)+~JcX) . h. (p·o ..1'X~O .l:LG L1.')':-')O AX (J).Jmh.'J{)J. Ol~ :ftc) C2J 2e'.X') ~'jfi:Jo'niJn b.)NJrrU3.x9Dn .)hn.lb X bJhBn~18r, cL'dn6' .:J !lJh6'nrn';lr~ bJh2fn.wen n:JEiJ6J 2Jmn h.'>3hJ2>e'i'\()' e:?J C:fcxJ·i!eXJ'/ == f I CX")·,2 ex:) + .f(:t). j'CX). (9jJt9jrdi2>.). Jc:'?>bn"dEinen: 'PCXJ:::' :fexi-.§~) IE:> QJb?Jnb("(!!'mm PCX) ~~5j(jnrL b.. /bh:Qn 4'c.:I.+L\.X) -"f'ui:::: +CX+ll~)..Q cr+L1~)- 1(1:)· ,Sex) =-HX+L1T)' ..cJlx+LJX) - -H2:) . j (X+L1X) -t- t (x)· g CT+L1.TI - f(x"),i]CX")::: (+b:'.+L~J-fC:x:.JJ·jc.:x-TLl3:) + feX)(a(X-tLlx)-.9CX)). JdJe-..\b PL':::C-t-L\1:.)-P(!.):J = -f(X+Ll~)-:f-(-::t1 . ~(x+Ll.x)+ fCxi, 2,Cc.c-\-~)-2(Xl , ~~ ~x ~x (h'::J j3 B~rM.)'dn 3::e.'>3~(]1 ~:Jh<Q'J h1no'.\ 6..X~O, .\~LI.xn.,£ J.\~nLEno.J2:o" hm;) ~M(1"lil.Jem6nu a.0n j tx) "3'.:JEi 1 jtJnj ~b)~JH'f1o'JJ X b~hb'0C!'2n c?j ~-f). lim 2e~ti\,:t.):= 51w, 2n3~60'J1 hm2 <;£'{'):)= fh)-~(;:r:)+t(X)'21'{X) l.x-x) h·(?-21. CdJt9.'J6f1. 2~ai'\3n OI.)bJillalD2:c::0n 8Jar~nL 5.Y\3mJ6~t:::'nL Eil'dSniJ 3Y1J01. ]. n. ec-f('JC))'=: cf'CX) . C9,,;]6'Y1o'J6..'>· h~2DfDO' 3~(\3<'r C3~wo'nf'\L EL\~ 5':lQ2:'no &mQhnJ' ..)2ntSfnd b...lh;)rnJ2.':'1c:nIlL a .II) lJJ/i::; V1 i3.fi IO.,_)G ':J8J.'>\::'mQ;> QjJmd(!'noJ/):)moL, hm2 :J~C?an2>(l "3~():1u'nnL bJhJmJ2nC!'(\ ":li!:'n(\!.., S'~~L· J. n, C' =.0 . a.. /onh e c -f(~)) '=- ct. f b:)+ c· flex; =. C- :fC2?J+c-t'6J=c-n.Z) . h - e .2J . cnJrMJJ,j.. a)~ fCx) 1:9,:, ~e:xJ iJ?J'Joduf1J{)n b.:>h2rY1J2.,,)<,?DI\ ~£ :r b.'Jh~'.1n ,.:.1JLaUb atr:h:u. J:idnfJ jJ bJhtS'nt"'.'JI\ bjh2mJ2..'>@(\ n.d6':16J H:x:) 'LlJ'BJhe:illoJ <5?.\ aCX) :rex '\= }'C':t.i·2CXi - fex) 'JI(X) ( . ~(x.J ) 3 ~('X.) ejdtljI\U:JdJ. .)c::>bn'(Jbmm: pc.'J::) =: to:) C!?..) 3..'>bY\b(\C'11'\Ol Cf>CX) 03~bju'n()L DJbhQ?n 2leXl "ttt"'ul-':E'tti= tc::c-t-.6:L 1 _ 10:') = i '\-f{x+.1'X)·jCxi- -tL:X:l'~Cx+.c.XIJ== i X 53CX+L1~) ,gCXi .aCX'+.1.-x)-jb:) L ,2er+.6):).i1b:'i x [tC'l:+L1'J:) jcrJ - ftr.)j(xJ+ fb:).Qtci- t ex )-j0:+~iJ-= 1. [(-fb:+L'l):i- fb:i)9(~i- -fC:x )l.2(~--6X) - ~tc)JJ . jlT+lI:x:'Ji/CxJ 2_/J1\5 Co ) C J TC':(t6)::J-g'(X) = i. T.. Kx-\-.6::t} - H:,r)q('X1 _ fO:). (j(x+6:;C -- (!(:C) . L:x:. ~L:t+.6.~)· >-J(T) l. .6:r (I . 1\ T. .:;1 ~lillc.."n2>.\rJf'\ (b(~~:HbJ (l~jll·~tI(]I, h",,(Y..l .6X-'?[) (9,:l Q(~J-IILJ UJr;j3.'J~('('2)(\iJ ,uo,)je:'nubnf)J6fJlJ1 d(1)nCJ(',(71 c:e'0u~J(','jnLl'J2>.JC <Plm~rr6jU. trIJrnk:kb C9. ..\J&~nll'J6:'lQ.:'''.\. OJ.'JmhJ3J' CJ\) 'Y=-tCXJ CjLJ6~hj"j 5...'J'.drnJ6.)C:;')J X bJh~ne''(Jn1 bmQ!'fYI x=fC-t) I:J~Wo'''cr' bYtJrnJ j~'<2n.) -t bJhtS(\~'dn 1 J..\(]nl) )'==-tlLPC-t)i hCfi"Jetl :3~fij(j()J !1"h3mJ6.:>en n:!Wo.J t bJ~tS'n'.':'::''dn C'?...\ (i ('f(t}))'~ f!C'P(-lJ)' --P'Crl ..ib~ iLL =- a'i . dx cH.. cLx cii C::?_\JC'O()o'~..). bJhJmJ6~f1L D.\J;IJ.J1bc~:16I\U m..lb.JWJ~ (-f lfL-lll) '= lim b') =- lim (.6-;y __ . L:::.'Je '\ l:>t.-70 1:>-l:.. L'.1:70.6X .6i:-J' 3f1FLVle""b. inhm:>,('01 , x..-='f'L-l) '3'Jsj()'f'') 5'_V.()«\JdJ~(1,:l, JJnC'mJ (\2£\ ':Jbj6jl£nll'J..3·.JJnLJ a.xJrII limf(-/:'-l-,6-1:}=.,P(f:), 6t--hi 3 .'lLJ )n n(JL 6n'(J6..)~l.j)hm2 lim CfC-l+-1'l-tJ--f(t)J=o, ...15':1 llx.~O,hmL:0 ~t-;>o . .)dn6'md .6-t-7O (tCf:ti)Y= lim (b~ . L\'J.:.\==- lim 6') . lim 6X =- f'[')e}.-.p'ltJ =:.-F1C-PUJJ·...plliJ. 6-1:~o ~':r. ~t:.-} ~Y:.~O /':,'r .6BO.6.4:- h.(2.(3. 'JJ6'\,()~b,). Q?..lJ~jndJ6nwLJ R~JEi 3o"jEnUba~ , lvn2 Llx:=: -fl-t+.6tl---P(t)-=FO. dtP~(ld(9J6.J, hrn2 OIJm!-,JQ:l lJ..la..lhm~n.£(l-" d..l'dnb.jU, hmuJ },Y.: ~On~N71(\ .lb .'l3J\'!'.J f:..-t-L7l.Jnu ()J()d£!:'-X..\ oJb@~L O-nLl:f'~n, ,01JrrNv.). 3atJ3.lCf) , 'j -= :f(:xJ Ojj5dUn..., '::J5j~JtEnJ L 6.JhtgoC!!''(Jn CS':, 2n1.Jn 2.J:ju'J~e'n .1:= :I-iCy) 'B'::JIJ .:Ji.Jru ':.JGJ'?"u~(U 'dJlJi2>.x1fIL, 'Yo::. feTo") 5'Jht9()~{jn· (j)j Xo bJht5'()~8n :fCX") "2>'JEijdru b.:.h3mJ6se::n..l c::..\ fa oH-O , J.\dn6 ~: -\ ')) OJ'jEdc!!\ J bJhamJCu~ (\00J3..\ ')0 bJht.5h::0'dn (9j JC?2lnen jj0i6,j tfme~jLJ i -f-{X) - fcXo) i lim f(x)-fC'Xc/ i X-Xo x-.;>Xo X-Xo 4. (QXj'= aX-Bnll., Lex), ::: eX :f. C L-l~'X)' = __ i~ sif)~~ 2. (.to2XY~~ , e-enx)~L Q:, XML x R. (a.usin~) I=- r==1====; 3. ':J") ern/=: n.:r n - 1 Cht:.N 1 Xc RJ -Ji-~C~' 0'\ L ':r..oi)/=CX -rq-ico< f. R ,Y.>O ') 9. Ca.LC-CDS xi =_ i l-f. (sin 1:)/ = COS X- Ji-I z . 5. c rDSX')' =- sin1: fa. uu.ctj xl' = _1_._ ,. (-I:£x)'= _i_ - t -t x:Z 2 CoS :L H. ( 02cdj xi = - _1----00: i-tX.:z, ·10 ? ... jhQ1-;JhO\/\ \ <l 0/\';1 ?JOJ<'!!rr0-".O() = a u: w a . Ib~:)i-\f\u d..\C'nO'l .P "A (1 + LXX' '\ :::: lim ~~ x·_ L'>'):~D T . L.'>X 'X- Po ( 1-1- L.'>X ) I :)hOl - JnOll\ \ 1 =- J_ lim ~(l .'X = Jfidd?>Ii'JC!!'lo~..lr;" =- i-.. 0 r> = .~. L\ X-;-O 6'X o,r: ~hf'\L J.JCN)') 'X Ul LL :c. 3. S") 3.\1'.~1[jf'r\01 J..xn:Jlb~f):l'Jh(\ n&!?'Jddnl\~ {)J{/lmenCf!: hmlYJ h = 1 1 113J;:)3u . H· L J:.Y:::. II' m X -\.6 X - X = I J m i -== i . X. Cl:C-+ 0 l::, Y LI y:-tO J'II, n:::1-Olj[)U (?:,lJ..lJd:)ml~3::)(T~·(\ ~mc:'iTloJ 'I:S.38<l~h(\rSI\J. e..l~·J';32>~m, hm6 (2)u,).M:)nlJ'~(\ (g(l\C!!'m6 J ~JlJa.)h()en,) h-0l3(\u (E':, 3.'l1\3:lbmOl J(llJf\ bJJ.:NnC".'fl..l5mO..l If). '.'l.'lK:?Jornm. hrn3 (1: h -'iY::: Cn-;-~)::cn. 5..lJ/'IJ3~nL 6.'Jb.'Jhdrn.'J6nlJ b:JwL (J\JoJbc3J~ CX(\~f'/=:('::c."<x:.J/ d.x")'. 'X+ xhb::J)~ n'XT'i-1<)C + Xn'i -= (h+~):x:.h. OJ oO',c:jQ:lO {S)J aj~3J5~')bf\ ~'jDdu'n2nu o..lbJn20'ilinL bJuJ?tJL a.xJm:tJbJ6r.m 2l3JD6j2JJ '-t C':r~)1 = [(efnx..-)dJ' =- (en::cy= 0 Bnx. (C(Bt,~) I::: ec.;t:n:x; c\'~ -= xO\· c{. :J~ :::: a: r- Cl -: J.,. (sin:r::)':= lim sin(x+!lX)-sinT:=- lim zsm'¥-'Cos(x+¥) =- rim Sin T .Iim CDSCT-t- AX >'::i·CDSX-={oS~. 111:: -K) b. ex h X-tD f::, x.. Ll X -;> 0 b c:r:.. .ll.I -xl '2. 2 5. )'=:. CDSX ~J6.:l(]'flrL 8_'>h2m~~~L 3X\rr(h~~ 8j()~jjJ nLJehn?JJ 2JCfJO(J) , hm2>n1h!'Cl.JO' 3J3myr)3J(!l1J(J) Y=<;in x - nu 6'Jh3m::2>~c::'n, Jb :1nC':?D hm':lQ:'11 li3'jDjdnn~ (ub.lh3rn:2lnL bJunL 3.JJm.':JJ5JOnOl, jJMrr<9, 'aJ3Q'J2JbJMJC? (CDSxjl=-(sin(Jt- _X-IJ J = cos(J(; _'lJ.(1L _ XJJ==-sin~.e-f)=- -sinX· 2. 2. 2 6. ~b~ ~h~ :JonG b~h2mJ()'j~nl..J 'aJL.lbJ6 aumhJ3n1J Q.lQ!lI1(J) (WXJ'=(Sif'lX\- (Sinx)'.CoS~-sinX·(Co5x)1 ::. Cosx·Q)sx-sih't·(-sinxj =- CoS~+5In.(1)~ -- -- - cosi.J COs Q.x. Co'S~:X: (j)';}X 1. (C-ti~)I==-(c.o.SX.\'= (CoSx.}I·sin~-Cosx,(sin:r.1' _ -sill<-x-CDSzx i_. SJrl')L) <;ln 2 x $ih~X Sin~.:r. B. 01'j 'Y=l1'1:Lsjn~. 2..l'd()5 ::(':::S~1")'Y CS' J 'dJdci11Q?1f\ 02)~b:J trnrL o.)b ..Ih2miJf\U b JlmL (J).'l5:.lbJJC? 3':Dj6'J6..1 1 1. i i (CUc.s;hx,i l = - .:::: I (Sih'YJ' - ws':J -/1- sin:<'-Y , -J 1-J::?~ l· .~ g. 1J1:J ~ :::: (ltC-CD S ::t 1 ilJ'dilFl X=CDs~ (2J bf1b~ ~<:Jb~6'nL JE0c:"m2i\~J~ 2l3J.:J6.JdJ I 1 l (J.;l.lifJ sx.) =:: (ws':1 i l -{ O. 0i'J ':l '::. Cl.letj;:x: 1 cb'dI"\O :c::: -til 'j . i i i i ----- - ----- ----_ ... - ( -L5 y;1 i t +td 1 y HX.: J CDS'2 y 1 i H. OJ':! :J:::. Q leeL;) X ~ J.J'dnb 3::::= cL:J ~. ':BJOSJ6.J L i ( l1LCC-t~XY :::: ---, 1+X:z. 3m3JOI' 'Y= -f ttl 03~5ddf\:> b.:>r2m:i2w~5b T E:Jh~2n. hm3rrY\iJ' .30lro, :f'(:U::: lim ,6 'Y' bX~ l:t::L ::e3Sn'df;nm: oiL'Ll=- !l:1-. _ flex)· Il'b:>en.) o«(~J --,>-0, /-inti) 6Y..-.?O, :J·O. od'X.) .'>hriJ :JLjlJ\.tJc:,('r)C? 2unh:J, 6x' O"'ll.l 6'::C.-,O. 5,,5'-, r!l~n·;6,:, C>.lI!"JoDJki'rOl .::,LlJ /l'J.:::: f'6: i· j:r HX 1.1:; 11'» ;1_\~",lJ)~:J.Jl ()~[jjo'l\(\LJ b.\'bhc:n 5.)~8.JooC' n:15.' rrln (]J1J.'jh.:'3nL b)bnm, mT'Y\:">J c!.lm?>.)bn 'j1Jjl.~\,)Q:'fnI':' (ldr~hJj, hrnd.\ L~.L-,D, 1,'61,..\.] (11'] -rrCIJ:J-:D, lill-i<::''(\J. hrn;] ;):JmhJ ~lJlJ.J.jh:i2,n '1<0hm J.lCCJQ.Y\f\ hn:Y\L 'jll~Q!'m('O JwllJ.\ ,3neflJ 1,;, '~'.C1. ~.~. ;)rlln");JvJ(~' 5·.',,)'2ln JmJ:'"" G'.)r;I1C'~L\ f).)!l;J(l'\,)(.'AJI;l, :5,,1-,:)1'::'" ';IJh.)6kj?,11 ' O~~Jr;:llfnnlJ r;/l,Iv<..!()/, :,,7 c7(n.)",',.) I, 1,,1-. Gn ~'LJ JbmeJ2>.l wb'rnhJe '3":J6.3rJnnlJ e.n~JI<)6o'f\je'(\.::l: WhL~ e~ n2f) ~(!'J)G.CdIJj(U dAL:rJ')b' 3l\\~Je, ci\) Ln2 2,O\<C:::ffiG'lI'i. J.l '2bG)~.)a'J, d. lex)::: f I ['.X ') 6 ~. .'>2 tJrre:ih2JilL ariD",3110'> ri x -=:. Xl.!::..')::. J. n· d X':::.c.x. dJ'2J.IU.J ~.l a :J , bl1b..'l b'nlQ!\m?u ~1~rJe:0J6.) ~~U -R:,:o6Jhfr101 5 o 3m13JOi, 1C::XJ '0:J()jll'f)j by.,2rnJ6~f).) hJ"dJ ~":1.Y22:'JeL1~. a./Jn6 ~'L')() n'lbJ6.1 ~3 d:JSC.l<:?~)J (jJb./b dn]Q':f) 1?3~5jt.J1l.s· ·:f'c~) ~'j5.'JlJ'nnL bjh.3rr)JD'jC':.'L hjnJ:J bJht?nCl:':'tn j5('f1@~:;2iJ 3mu'JJ":1e'iI :fC::l::) '~~5.ddML dJ mhJ hndnu b'.IhdmJ6j~n .)J6'Jh~nc:.n2{\ IEj non j"eX) un,33ffil!!'mmn JC2nnn'ClOJ6..\. J·n· :fIlCX)::-[:f'c:tJl J ,)b.J~rn2JrI'jhJCE 3j5nlJJCk~J6') -HX) il?J<jldll'Mu LljLu8J hfYClf)LJ b.:lh()mJtje!:'f): .flll(~) = [·f/lC~)JJIEJj·d. 'jJJWJ~n hnorlL bjhdm:lD~C'JanL j~UjbnIJEij3.5c:' 3..\2mn.':JJbJ6.J hmdj':J~n hnlib3Jdn: .fIvC~}, JVC:::t) , . , n -'Jhn f!n2!C\u bj,am.J6~~n .f(n)CX) Li123mc... n mLhn Jc;nb,,'CJ5J2d. o.)h~) .),3nLJj, J:Jmh.J, d:JGjd3 ~..'> .). d· n -'Jhn hn 2.nL b.'lham50~Q:" Jllu, ':JJU,,\6.ldnWlQ , "\UJo' j ~b, ,'J5j3.3b d, ~f(X) cPt C'x) clCh)j-(X) , , .. . , ~ X ~ cl ::r ') ci ::t h. 6 2S-j Lfl3v:J3n. x 0 fl~h~I1Cl, :Jome:0() )1= fex) '31f1J6:j(J'1l1l1, SShem~Om() JOI'lJ crn~J(vJhn M:lLrk'llCJaOU ( uS, VlJDhSCme, 3SjLOd~af)1,) fljhl8ncn, m':J shL~~fTlQh Xo D'Jh120cOlJ nlj(J)(1 (1:0- '0 i Xo+o') 2ne.s2m) hma ~ex) ~ ~cro), hmou XE (Ttl-~; 10+6). (Q,~6::!LJ()nL 21l('f<l30X~0[, 8sflJna':JUll, f):JhrJocldn 2s:JLn3':J2n .'Jbme~J. 2.sdu(l~anlJ ojhtJOCf) sC'ri5n26JJJ ::X:mtt)( - Cl(j1, lxncffi (ls:1lJn<l':J3n 'J'mac<)O) . .8 fl6f):J~2n· Xo o~hb9()CL ~bme~dt'J ~= fex) '3l-JIl:tD'nnL ~Jhem6IYl)n J5~ ~J(:Jhn 3n5nd~an~ l .56 , ~~scme, 2(1onJ~2nL) c:Jh!9(Kn, m'j shL1Jfl1~L Xo njh!l'ncoL nL.jOln (1:'0- b ; To+ f) 2ne..ld m , hm2 ~Cx)//-¥eXo)' omIT.) XE(Xc-b·li'oti)). ~Vj6:fo'nnl, d1in~30xma~L 2noOJ'janL njMIlC\30 2nilna~2n jbfTle:J00· an5r1J::J3nl, b"jl1@nCO JC'()on2ifi)~J 1:.rnin-OO), h01cm llf)6n~2fl 'Jmin-{\(JJ. J:l L 19h ~ d ':1 a f). b~h(JnClJ jli'me3~0 "3~6:t(J'flnl., j:1L@h~J':130l o~htJlncn, 0"iJ nlJ sh01J lJd jlj6j(jno!J ~5 3SJlJn2':Jdf)l; so 3n5f)a~an~ li.'JhL9ncn. !13"J6:Jo'onL 25~3CiXmaJ6~ :J:JlJ~M2~dn~ f)Jh(90CYJ'iln 52 1!J':J6jtfnnL 3j!Ji9ilJ3'J3)3n j6meJoJO). '1:1 ~ 6fl',B & J. U'bSeo~ 1 hm2 G1'J -RJ!J~tJI'lC [a. ; £> J 1J133:JEitf'bJ o,S5L5J'b('3h':JQJ) Qj'jf5jur.. l J3 W3dJ6tf"6J <!' 16".1c.m~[., a)J3()~ ~~ne3u e.~ ~lJ'nh~l- 2 bMJjojCm~J6~} as'd n6 JIJ dll(l~3ffJ(fl'la~n 2()()(lIJ6 OJ D ,Hi jj!.JtPh:J <1':l3nL. b:JhL90('J6'dO 056 1JJ62.:JIirEnL ~mcmjdfb~. 'j ~trdX 'j rni n Q.' o 'Yl1lin X mAl< Xrnin ()1,%ja'nn~ ~5hem~ndln jjLl9hJ<j~f)L SALJdm60lJ J:lL1nOd~C 3nhm6JL a3Jdc:J3L, 'ij jdeJ (30 (TjjmhJll0 ((!jjh3SLJ O1Jm~d.)). mlj Xo b3h@()ct;JO ~ eX) ~lj5jo'n~~ S:13L, jj~tPh13';1dn, 2Jgn5 t(Xo) ~b .5{) 0hljdm~u sli ~'(X.01:::'O, esagjOl'l'.1dU. "':16ej 3JR~~6(l'1(J) 1 hffi3 (f)'1 X 0 lj1Jt9~Ja~df)~ Ojh!:?OCtK.l 12.5 fl{T o ) clY1L:J6mHJ 8J'2()b -f1exo J :::: 0. 3()21':1cnubllm01, &.3JC(1a)M~) hm 3:-0 8s::lLO:J~.1nL ti'jJ)~I)Cf)J. d<1~nb C1Jl1LJd.J6L., ~D-()L ()Ljali1 (xo-s -) X-o-+-'b) 3nes2m, hm2 -f (X) ~ f (Xc) nmo'u X E: (Xo- ~', .'ro-+-6). j. n. acn~(L JJ 1 2nes2ffi'ilO lJh~Cejd0 'Jt9mCffidc\ -¥ CX)- ~ (Xo) ~ o· .52C1£:9m2) o'bJe.{)S hm2 sC'li()ab~S ane0dm~n ? 3Yl:J6:J6J : f(X)-~CXO)hO hmoJ Xc(J:o eo X-Xo r} U.sMJbOo' ~()3()1!'~01' nmJ lil'n {(X)-t(Xo't~O ej X 4 X;- x-~o ~ f 2SChJ:I, bJ"h3m~~cCl!J JhLj~rn~oL dJd(T) n.rh1.4QJ~L aS6'boc~C() 'E:Jr:3.she:JbnL ~hn X 0 ()3h lfflc30 tl3JD ;0 3mrn~, hrrlJ 8shlibjciS J dsM3Jlis <b013 h36fl es O}~nBlm6' ~(!1J.shnti IS111c6n ~6eS nB6J . &arlxsesJ3, 1(JJi,3O<lCl1J eS3JLj36j(1h hmJ .f.'CX:o) ~ 0 ej ~/(io) ~ 0, LlJnes6JO' ~t:ra.J =0. C236n~36"5· 033haSu O1jrtlhJdsu s::BlJ ~J4e:12ln QjmJj~hO~(n '3noJJhLn:- bJhJm16Jen Ojjt5:1lJ'()n~ olis~o~nuSeAn Jju1Yhj~jJ()L ojh~OC~O oS~j6'Xn 2bJin .l6ull'nIJJl1l.l I2"Jhdr/~ .:1JI15C:JC'Jhn.l ~ o x JlJ o:,S:J~fl ':1~~J(('T\e 2lsamaen()Sh~('OoL ~~hasL 01:lml'lJaoes6 ~J 6shamJ~~(n1J ~~J~rfnl1'jcn '2n6SShl>l\e.SE . ~ J6"tl'd?lo.5. bSr.3m~~1j(olJ O~C(hj6 t9mCtnc.) ShJ5 uS';4shnu() 3l1hP't6S j;H)~jUd~nL shW~/T1 6nuJU1~f)L. 8JDs(.oO',se., -fex)=x D ~"j6':1U'nnL(])3nL .p1[O)=O., 4.rohJd Xo=O J1!SJ J:JLtS~~~:lanu ,l)jht"nco· l7l:lmh1a~· 3111:l~5lTll f(x) U2>~6:hJ'o~ ~bj3j6'().5 [a,·,tl UJl>dJ68'1b~ , DshJrnjaseru .52 1>J2>;J~6'tYf)lJ ~fIl3.k ~MS bjht8oc~o es f ((1):: -¥ (~). dodn6 a es -B ~jhl9nCld1J ~~o!.J (\Sh[':1~J~L -OLj010 C QJht;'OCfl ., hoi~ -?' CC) := D esa@jm),J~0' 3 <n-:l3J (1) -, m es uU ii'll).!!), 'dJvJ~sJnlJJe) reX) 13c.:16:JD'onL !1doh~.J[A) es ~eoejLo ~fin~36'j(rn3j6j) fa.; £J hjQdjOtJ~j. ZlSo30bocmm (ll~O '(l~dOlb3~jQ: IJ m = J.t. s J ':}~~(1)h3.B.s'd(11 LibsenJ, -Fcx) d~edn3nJ es C bjh&o(:n~ r.mc'dr> rt1~:Jnd (f)j S30e-ffiOi a. es .g - .l~ I(lm~n1. ae.J3.sh J 61~WOJh n tJ':Jhcl'OCO. 21 tn.:tj.t. ds206, ~C(1):~~(£) Joh~L 3dd!l' ~dll'nhJGn eJ ~%n d5rl'B5Jem0'J6~esr In<n- j~cnn 2soG/J dm(!,~33.5 [U.).gJ UJo2jo'&oL hmdX()(!'j Ii ~(12S C b:JMfuc~~. 2J(Jn6 ) libseOJ, C tl'jhrYo(() (l::H)~6') J:ll>tf"J~d()lJ o.:lhlfucnV'. (/j~hdJU O1jrn~j2nL Jscn(fl es3J !J~?Jbt)01, hmd -t'(c)=::o. l!I3hn~36S. hmCnL O1~I'II,,~aJu .d% ~jdej'3n o~m.?.:'£:9hnlj((l "dn6'JJhL():- 01:1 ~J'k~mj~ 1B,,6;§trnJ h.rn21 rtIh o.31\rfoc10 (jmc 26'o~~j(m~~1dJ C'~X!I1~~) dJ'dflc Jd b:Jn19naJL 'dm~l1lJ I\~ lJj~~~L (\I"JOM 6'.'~6c'1(n, hPlJcnLOI?lOuJCJ' 2lhJ~;n~J~c1n ~:JlJJ~Jd('jlJ 151h~n<:~fl M3C1A:.Jen 4bj~C1 SALJo'nbJf})') C':lhJOL jcJhJC1(~MJ. ~ f(Q);:;f(~) o - ~ - , . CJ- c x G'l :lmh 1.1 ~. !,,:f~.)Ch t ~(X) 1~6'1U'nJ ~ b~3.J6'nJ La, B] l1133j5ff<b:l es f)sh.am)1JfTIJ J~ L32Jj6"~n lJ !1ll\'?l'JC IJoaJ Kjh~oc4}n. 86'3n&' a. es .g o1h~n(J21L ~(l\hnL njhL1a3~v nL101f' G bjh~nCn , hrnUflLl7l~n1JJtt .seancn ~:l6"3aJ cjl'l'l,m~lJ -f (£) - f (tL).:: f'lG) (£-{L) . 8 Qsalf~n\1:1a~· aS6~ObO(mCJl t.s.1bdsM 3~6-;f O'OJ <:l:)= -¥(~)- f~f.~-~(~ (x-a.) .. ItbJenj., hm2 3!J ~':S6':tl1n.)tJ n~.) [a. 1'8] lJjd3j6c9l6:J ~o~~jlft1 ~J J;J !jjaaj()&nLJ ~m~~c 1nD~ OJh~n''10 f)sham~a.H~n. 2aSheJ JdnU.) , F (Go) = -¥ [a.) e" F (~~ =.f' (LL), j·O· f(Q.,)::F(~)· c11JJbJ'eJJ.1, F(X) ~~b1a'O.> J11s~3nC3~L hmenl. cn3mb~3l'lL ~~:J9"j .:Sl\hm~J1J. J~olfm;], ().. es 'b b~nd'n(:1.L ~fIthnlJ l\JhL,1~:J~lJ f\l,~n C li'Jhl9ncn, nt'llJ Flee):: 0 . 3Soh.JJ FICX):=: .f'eX) _ tC£)-¥UV . t-a J·n· -fl(e) - fl~)-f(a) =0, -0.. LJSnesb.H)' ?1(!,J~~(m~<n ~SI.JJ2cl'~l1'.1~3c 9iln(l'l~.)L. tJl jDn'2~6 .. · ~Jahs61n1J O'lJ~~jaJL J:l?>lJ ~:J41!~Ml a~(11J:J19hnt:1(n ~nbJJhLr}: - E!sn3mj ~n ~~S:fvnoL 3hJ~(\¥bj Sl!'~~~C SJ~nLan:lh m" ffjl\~n(L. 'Bmr.OlJ ShLJ~u ()WO'Ifl t:Jhtfom, htn2~O 3J~,~nCf\ ab:l~f\ Jd mho ()~~19n(01J ~jaJjhO'lj&Jcn :rffihenu 3JhJCIC!1hJlJ. 'j ..Q+.?"":...--;J'----'---""--__ .,..-~ X a.rhQ}(Jlf") aM~Ol, ~"J(7)b':1ho jfJ1'~nltn:J6l9o.) tj~= ~'(c), drnhc::f'lo.'> In t~))= -r:(f~-~CLI ., (!l1jQl\J6.tJIHJ O'\J",b~JneJ6 ~~j~'Cm30'l" hCft3 i8d ~ ~~ 7 LlJoes6'J1Y ~S~3 6'00. ) h. tfI d cl= ~ fj ~.(). 3bS10 es ormhej ~JhJdl:':1l\6'O shruo al~m~dJ· ~Ol:t~Jltl ~ ~C~) s ~f(;r.) 0?J~6'-jO'03~O shnJ6' ~'~3jlJ6n [a.,.gj uj2l3:J6'6''bj es bSh3mj~se6'(\ Sd lJj213:J6'O'OI. :t/l'l~JC ~oaJ l)~htYClC'EO 1 5c3JuUlJ'5' ~leX)::f-O. a~o6' 0... es t t)~h~OCJ~L t(JmhoIJ OJhl,~~J~iJ ot.:bln C o~h~n(o, l\~a Jeooeo-n :Jj6J~s !5mCm21JU -¥ct)- -¥ (Q) -fIco ~ (~) -3 (Q) =. 8 1 (c.) . eS36~nl)'~~0 (!nsl»h.s6'-!lOl. l1)Jm~:Janv d6'J(cn?ln~hnJ fO<!'l'IEle Jd1.iJhJ ~~J a.s~30 t M('mtn ~'Ue~a(\ £lS3ba... h:J ~':16';tttn.} F{x)::: reX) - feb) - ¥ (Q.) (~eX) - 3 (Q)) . ~ (~) - ~ (Cl.) ~~En1~6' J. SfaOCO ~3UJ4~6"jOO..\, hmJ ~.fa~u6"lJnl. t:n~mk~aJ B'JhafllJ(!a~6u ~m~nll O1:lfT\h:1Jo.l, 03 ~Jhd~ ~~~C1lb~B.jL ") h~U".j 9(;):)::= x. (]'l~mtqJJ ~ 3(1);0.,(7). -PCCC) es 8(1):) ~tt;J():tdnj~o oshdP1j~e60 J'~nJ6" Q., b~btJn <!"I\L hSl:4~ Jne.samlJlO 1 lllfheJ, 12~1JsdCf11J m ~nOllh 6' a.. 6'Jn dlocouJ ) sd.JL(J)..s6':9' (X) =* 0 . ~cni3j~" ~Sft.€J j3nIJJ) Hm -¥(x):: lim 8(~):zo. a$~n6', al:3 s~lj~"!L %C0J.5hO lin) -f/(1:~. x~ Q.. Ox.... Q. . r-KJ., ~' (X,) .fCX) . I' fie) 9 I , ()SHJM~lJ lhC135/'100' 1m __ . e.s Je30Q{1 :Jj5~d') ~mCi1l6~ I,m d::r:) =- lir'l ~ . x-+ 0. SeX) . X-+Cl. 9(x) T .. -l1l. gIC:L) eSd~~OtrJ~J. 3(7):f3" 01 , X .rltl50~6c:1(n JneJJmL 6J~oWnJhn &Jnt!(lcOJ· f (:1:1 ~~ g C;X.) 'J6;f£fnJ~~ a. 5Jh~O(~ () dn?>J6n ~(l)0l 0-I1U lfulco a60':lj6J(m~j~n· a..l "3nE JL ~~6J1tOJ~n td6"j dns fi ~D~3jt960 a. oJh6nc'aO ()'. jm~o!J O"ljOlkj<10L dcKnlh lL eJ X ~hr'nc~?>L, ~mML ()ShL~~~~l" otJmn c o3h~oco, I\ma -rCX) - ~ (aJ - -t I( c.) 8(X)-~(o..) - ~I(C)) !Jsoes bJ (j -FCX) _ tCC) . 8(,X) - 2'(C) 506'JoeJ6 C amOlJ~l.Jj~~(00 CL e J X o.ih~~a~L, ~mhnl1. , jJo19m3 ,00OJenJ C ~ CL hrnlJ'J X~Cl.· sJnLPm3, on6's Q'mC(Tl6f'1L UJ'j~d3:Jcq,~ '8~33()d(()J 6:'J3fJjhrn~ lim t(X) _ lim -fl (C) . X~(l a~) - ~a. glee) 8S0hJd, 11 m -fl Cc,) OOn~~..l hJli lim ~IO:). ~.n. lim fCX) __ lim -r'eX) , ~-7 (1 ~I (c) 1 x~a. 3' (:X:) x.:;a. ~ (;:C) - :(-)(1 g'CX) ~Jon~?loj· am~3J6()(n D>Jmhj(lJ Jbnrn~j ~'ao.5ov 35~CbC'~h:J(m(3~6/.J. SklOlnjJ m~rnh~a.) UJdshOlCOJOl1J 00 t9nJol.., ~u 6~ ~ .. C'~h~crn~.:JSnLOl~OLJJtY. 00 B~(){!nmh"u O?>mh.a'tiQ1l.) (11Jmkjd.). ~md3,)0'), 't(X) '!~6'd(J'o.}u Q., a'.1h19ncol. hJ()a~ aoJ3m11' lIJJ-RSnJ bsh~/'O~~~(j~n n, hQ~Sdej RrOl&'Oc1l· a~(l(;, J2 dOeJamL 6"J~nL2o~hn X bJhtPncrluJ (Tlj{)[, amCld~66':J6.) a., eJ X f)~h{j'nCl~L 'aOlML :1e':JJJhj oL~£1H) C t).~,,&{)CO' hmacol0l3nLJ(J PI(· p"r. p Cn-il c 1'\-1 ?(h) h +(xJ = tea..) + 132 (X-a.) + ~ (x.-a./"+ ... + T Q) (x-a) -+- 'I- JI0 x-CL). (i) 1 ! 2 ! (h- f) ~ h! ~ esa(9;Jl1ltJ6tj. 00b~(')b(\c(T\(h "W(1)(') JJ. h(\lib~f), hma~(nLt 3..H)ntJJ'hC!~h.:J~J (9m(m~neJb .£1((11' Pile 2(n-l) n-i JL n' -r(~} = 'Ha,)+~ (x-a.).;. ~\x-a.l,+··· + I (Q)(x-Q) + -(x-:a.) . (2) i ! 2 ~ en-i) ~ h ~ ~3JG ~6'ej OJR3<J6ml1l:l hrn2 ~ es X ~mn\lL JhlJNn~L "l.:JQln C S'Jili90C(l, hrnc1cnL O);)f)Uj(i f (0)( C) = JL,. sdowOJ3nu eJ3/) j() JL() hffi 111 X O'Jhancn es 3.lC3oli\(m Q1 1:. J h- 3~aj6"l9(\1I ~:J2e~~r. eJ~~.sh:3 ~~6'.1[),()J (n {'(i) Q/I t -itt:) h-i ~ )h fet)= P(i:)+ (X--t)~~(x-t)~···~ --(X-i) + -(x-t . (3) T 1~ 2~ (h-t)~ Y\~ l~) L5'mcm~(\lQs6 -RJ6'LJ) hm2 --pCX) -:: f LX) ,O(l1crn (~) eJ (2) d'("(I'1~j~n.eJ6" 30J 6{J(Il)~0l J hm3 ~ (CL)= -?cx). dJ'dJuJ'eJdj ~ --pea) -= '-P(X) . 3she. J JdnW., lJbJe(\J, -pet) ~t.lj6'-J(jI\J ();1G;Jbs 5J"dmJ~J~n {\d ~~c~e~~ j nm3cnG am(mJ~nJ (l. eJ X. Sdf\lS'm2 ~ hmCfllJ aijml'lJdflL ~~Jbaje, CL es X 11rt1hnl. ()JhLj6j~L. tlL..'laln c., hlhJ f'(Cl=O· 2SchJd 1I ) [ f II f e 1;) Z ~ IIC·t:l l f'(i:l d'etl+- [f i ~i: (x-1ol- tJ(t~ + 2! (X-t) - -1-1 (X-f)J + ... l 'pC\')C t ) ( h-i· ten-ftt) (, h-.<.]. JL ( J...)(h-1) + l x-t; - ,-X-i} - - x.-c . (n-~) ! ~-1) ~ (h-i) ! ~~~nQnn t:}:llJJd-R6~?>()J" hind tSa L9O"(ffi6l)L &hti~J 3bJhnn ~3~C ti'.Bhn ~Jmf1tl~'J j 8~.) I iO mhn 2J01:>'Cn J , Sao19m~ I tcn) 1;) h-l J..t h-! 'f (t)== (. (X--t) -- (X--i:) . (n-i) ! (n-~) usn .s6"lt) ~LC(,)=O ~"'Cm~nL c3J(»!JJCnlJ&'Q(i~60cn eJ3JLd3000l,hma fCn\c)=J.L. '2'~ ~~6' J. bjahlJ Jr n (X-}::: £(I1)~c.) (OC-CL)n c¥~(\Cmhnl- ~ hd~dl1J 6J~(7)nOln bJ3hf\ ~~:ne21j. n ~ .. ~j6N~~bJ' Ul~ (1) ~mh~~CJ'CJn S:>OL":J~lTl Q..-=:O) aao aM~J~[' UJb:H.I -¥(;x:):=. -¥Co)+ .¥'(o) X+ -r"eo) X 2 + ... + 1 (n-n Co ) x tr : -¥CI'tC)x h i ! Z ! ( "-i) ~ n ~ , use.JO' C shnL 0 es X b':JhU'OC)6L., 'amholJ de.JoJhj hdt"JO' oJi'-!kIcn. SJ ~h~~(SlJ a.rbanh~bo1J ~(1'\h(}':10 itt30J. en ~O\h ~ d J , 3n1?l.lO), -reX) t\Sn2j lI'jsoe~~ bS~~{T\:las~n ~'jf:tutlJJ. JJ ~~sCJe(M: 11 -fex-) d"JeJn30J aJ'~Ob e.s 4lbM£fl1e "J~n6~· h~ltj -F'{~) -:=.0 , 1) t ex) S"s~c:J~S~n,) 8J~o6 e~ abmc/TIe a,,~n5, hr'lIfJ -V' (X)='lO, 3) teX) oShslllheJe.oJ ~J'On6" e.} abl'lll:/\1e ~b'l'o6 t hMU'J ~'Cx) ~O, 4 )C]l':J"~l(X))' 0, :1J'dno ¥~) ~nes<!nJ , 5 Ol~ ~ ,(,.-) < 0 , a.fcloo f(:x:) ~C:2~JenJ. esacj'~r\o'j~~. i) S:1 ~6"eJ 3s7?3jom~. h"d: J) 01~ ¥CX) d~eaf13f1j, d..J'df1b f'(x)-=o ., a) (1)~ .y'COC)::O) dJ'dnti tex) Jj~Jn3n.). J) bnOJeJeJ~nL lJJdJ~O'l(n.Jtlll'l~J ~~~J(me oJamc1~f\bJhJm~L, li'Ji-.2m.J2':1UH, OJS'bJibl!'3h:J ~neJS. 6) go6"J eS~J3nu luaJh~(I1Jbm~nL eSlJJ3~nLYj~(J~ j() LJJ~CLhnL..r)J ~JiQJbmc1l., hm3 JIl'IV'JJ~Cl'\ ~c:1S(jef'\L S'laOLanJhn Xi eJ X:l. oJk&nC.'J~nl.~3f)L ~(Xi)~~f (x~). jlJ 1n .s1-1S, hs(.o.>6" £!Y'sohJ6-!Jn~ 11l1mh.1anl. ms6'JbaJe X.1. fh X J.. 'dmkOt. nJhLJc!j~J., C\LJlnO X b~"t:9l\dl, hOld -¥(X.1)- ~(OC2)':: f'(~)C~::i-X2.),jnhm'bflm f'(:t.) =0. sJrnYmJ ~(~i)~ fexl.). 2) S:f.J(J' jn~n OJ6'"nc(\ .1&~OLYe.1&.> bJh2m:J!')coL 3.16tJ.lb<!13hJ~f)L LJJ~';1,nJ("CfI:J. JJrnilJ ~f) CS~~J6'nOL. Gl~mhjaOu a.)am~jo~ntn. d..rhmotY, O')~ -¥(X-) shJ~(jc1JeOJ, aJ~n6" ~-cx-) 'l ¥CXoJ, hmlJ'J X. 3'X 0 eJ ~lX) ~ 1?CXo) ') hnHYJ X < Xo . JarLPmJ, fl\h~3J ~3aa)~3J3..}'d() ~(X)- ~(Xo) -----'iO. X-Xo t1\':t Jd ~l9(f\(m6j<1l\ 6St.}3JC<n <O("?l.ihq,j? hf't\lJ'J X.~XA, dn30C'JMl, h(h<l tIGXo)-'lO, hJO' Xo btlh19f1.('f\LJ !iJ~nLlnJhfll~nlJ aJ<1f1l fin'd6'JbL amtY:Ia~c ~~x~j bJhdmJ6'JCl1u S .r~sh~fn~n!rlf'r4i3JlJ. Ol~ -¥ I(~) 7;- 0 tJ ~:L ~ X 2.. dm!t.1a~<n ~~SCj e. nL 6~nL..anJhn ~hn !Jhtfn(nJ 1 aJ'd b. ~~nL <n~mhJ4nL O'lJ6.,baJe. -rexj.) - ~CX2.) = .f? Il~) (Xj.-X 2.) ~ 0 J ~·n· ~Coc") ~ -¥(X2.)' .:Iu ~n on~o,,2>L- -?CX) ~~6jclnnL JhJ{)c:J~Jem6JLJ. 1i ) 3LJ J"Jb'!tfn I(ljf)d(~~J eJ8tJ:1mteJ/; .s6'J(rno(\~hn 8u'5J'm~o(Jl, So (-fc:x:)) ~~r oJ :htMu 3Sobnc~o<n eJ ~1~j e.5dl9jfl!r'J~~(n 2 J J~6jt9(lL ~Jdm::JJ6j~ocn· lJJbjce(l'l~h 1 ~~ae~ 6jCl~Je: - .p(x,) .shJ'bheJeru 8,",~06 -eJ 30rn((1le 3.)4(Jo6, nmv'J (--¥(X)) .5hJ j(j&JeOtS, J!J ambe~6J 2.J'(lo6' eJ <ibinanl! (V~n6 'hmdJ C -tUx:))''lO J :J on· kmlJ'J -F1(x)~. 4) l!.J 5") jVj6-:ft?:J~n 20'~nu'ejbnJ6 bn6'J j~6'dlYj~nL d.Jmhj 6Jff(lCJ~OL alJ3-'3lJJe. 'a:J 6n 'd 3b.) . Lt) e J 5) J'~6'j(j'Joan 8m~~n(n !i'f)6JeSeJ~j6nL I(JJOO':l()j6~J«() 6'n6'JeJe~n ShJJ uJ4JhalClU(n. 8.s3JcnOlJe ? -¥Cx)= X 3 "3~6'jLtnJ lh~eJf.nJ aOJ~C (]!J3nl" <3J61J~C'l~hflL sh3~n, (!.1ohJ.1 ..pI Co ) = 0 . ~jon~?d) J. al't\~t~,)o(\C (1)jl'\hjaJ'dn !J(\~~~<> 11 ~(~]Jc~en(( Sh 'JjfldCI~j ~~f't~(m~ ~Oe:BnOl ,) Lf)ahJ~C~ (/. Es3JcnolJe, -FCX-):: 1.:~X ~~6';;H"'nrt 5Jhamj~~cn e.Je:J~n(JIn u Jd ~~()-j()'nnL 3s<illJC?lC"3hnL. ShilL ~"',?>jC O'Jh19oclln J (jJ6nJd :JL ~~6'jrtnJ JhJ<.l lbhe.5en at11:JCL tr.J30L OJoLJJ~~~hftL Sk1'13n. 3('1~B()m 1 hffiJ 'P(X) '0~6':flYnJ Xo b'dht?nc<b:J oS3C(\uJU t1U'~(\L ()11~,i;L I,_lf ~eJfi l)+((~ltj} O'l~ JhL3~mH To b'3h(9ncf'll, oL]O\o [1\-~,Xo+o) dOeJ2rn) h(1\~ 'f(X)~OJ hO\u'J X E. CXD-o, Xo) eJ -fCX) .//0 I hrnu'J X E (x, dX'o+6). J~j3j 6JolIlJ..,Q,L"3n j~.) ~2mad(JJ -" (\l~3(;11~ 6o':!JoLJ n+4'-(,S6" II-C" -C'bj: O1:!mhj 2J. 3V1.:t3.J() -rCX) ~~6"JlJl),) b6hamj3JnJ Xo ~Jn~nc()lJ /Ml\dj dO"J8I'l1~ n I1 aShes, ':JjuJk(l\J, lh~oO)m6' :;:'0 O'~hL9ncnLJJ' o(Tlcm Jd O'jh!l'fl('d(l (Jan u.Hl~3jcPnJ. dJ~06': 11 en':! -t IC x') Xo b~h15'nC<03 3.>?l(OlJJL O[)'3cnL 6()~6!J 1/- f( -&6 »)+I(-CtJj 1 a,,'dr16' fiX) ~'j6jU'{\.)L Xo e'Jhl5'oc"Jn 5:l~1; 8l\£ina~dn., 2) OI~ -t1{xJ To b"'jhC9()cq,~ cJ~,nLJJ;" ()O'~C()LJ or"llJ61J 1)+'<- e..JO JI-~ -t?J~ 'J .f'C~1 ~"'6'-j[)'nJ[, Xo bQhL9n~ JJi3G d.diA1a"J2rt, 3) Ol~ .f?'C'l:) :Xo o~hL9n~J ad&()LJJ~ Sh (\O'~C()L 6f)~J()f..Jl aJ~r16" -t(X; '3~6'jLYI\JL X-o e'jhlJnc'dn sh Jj~l jjLt9hJdljJn. esl1@~lYJ6J. iJ 5OJ:f3Jcn, (Xo-~1%+8) 0[..,.10\0 2nJ2mJ ) nmd ~lC)C.J ~ 0 ~mu'J XE;(~-Sl~) e.s ~I(~)~O hmL1'J Xf(XolX,+DJ· 3C1l£JO'" X:f~o Jd 20 eJdmL 6J~I1Lanjhn {lJhL9nC()J· aJ~(\6', (!'IJohJ6oUoL O1JrnhjanL O)J6'Jb<J.!e OC (2J XO 3rnho/; 1 OShL,j6j~L. ()l~OIfl C aJI\l9nc(), hma -? (xl- ~ ('X 0 ") =: i?1(C~' (x- ~). hmL)'J ~c <.. Xo I ~J'd(\6' C <.~ e~ jnhM~f\lJ' ..pICe) ~o· sJnL9mJ -Flee) (X-Xo):rO. hO\LYJ ,x):rOl d,/~f\ t C 7 rrb v J"hm&o 0\ ~I Cc) ?'O 1 llJ~h-J 3n6J"eJ6' sa ~jd~~J~n fX> Xo 70 , j~nl9fl\d Jd ~JhJeJO' .f1(C)(~-Xo) ~D. 1·n· JC'O()~(Jcn JneJdrnL 6'j6oLAnJhn :JC oJhcff\ C()LOI~nL -f ex) - ~ ('.x:o ) // 0 u6'~ t LX') ~ t C Xo) . hJ if [;ornhJ e I1dJL.. 6'n '26' JuL 1 hm J Xo tJ'Jhc9nC'drt ~LX) c;Uj6'"jU'nJL Jjj~ d(H)()a~an. 2) al9;)olJ'e~~ cfoJCmDn~hJe JO (--¥CXIJ '3'1S-NnnL c3-J6"bnnnOi QS i)-ilL 3J~Jj6j60"'. 3J 6s~cou eSVJdrj'Mtrjoc.se 3rl~':1(n\...baml1l J d J 3 J cnOlJe 1 hrnd sC"6""~6{l(n dl1ej3(1\L 1l1h~3.J 6JbBJh~rt -¥'(X)/Q. 3~""JnfJ ~n~n(''.~6(]) ,hm:l -!?CX).( ~CXoJ hmlrJ X~X.:l l'J -PC'):)") ~CXn) ·htllllJ X7'Xo· .1lih33G-\ Jd ~&m(m~ IOlJ~J61l o3J~S6j3J 7 hma Xo shJJ al\6'1\2~<1f\u 6'.1(-.£9(\(0 J~:J(I\"j ~n- Xo Jh<lJ dJjD(\d"'j£lnL ti'JhL9n(n. J,t'\. :Co LlIIJJ JjhLPhJa~anl" ~tPncn. i2 ~. '9~1LJ'no" a.s6'1JJ~~3h OU shOll oL~Ol 8'3h!90(,~I,', "m3<:'~~ ~olJ' oa~6':t1tnn~ t)Jh~m~ 'j(1 So In .sh1"Ml3"IJ JQ oo:JCnl. &(T\co,) J ~ h n L:Y01':1c ojhllnc~H ~8't"t3~~ b ~ ~J' 3,JL O)j(1\h3aOu O).s Jb3~e, ~~6'~iYnSL :l:11JLPh-~.1~dr1 :Jbmcme SW01 ajl\L3l\(3~180 1jnJcj~J l e~L. 8s2IhJ3 't hm~O\htf tO~am", ~6jb~\7l, ibman~h(7\(\ ~h(\C/n~~cn' o~hC:Pn(n ?~lWd~J J~ Rim ~~l.19h~a anL ~jhl:9n(O. oL ""'':1 hM3~Cn ~n(\{9n~~(o o~hlPocnJ j:fLl9M<1'::1anL ft3htPlI(() es Vsb:J,e~h n",33(O - 2n6n2l1janL ~ d".1tnat:laOL, ~6'eJ ~J3Je3n6mcn oI\6~3~J"j Q1jmhJ:1nL o.sdmj:J6jMOl. atn?lO~~6l'1lO'l 1:IiJzjh3d':J2flL J"M,j~m3nL ~neJ3 JhOlf\ Usj(lJn()LfI jnh01~ 1 hrnaKou' :ticMej aj 0£l6:f1"'OlH. a:lrnh~ hf\30L b:rha~:l~~(nL e9jha(\~l"dn. O)jfnh J as. S01:13.JO'l, XO ojhlfu(~n -¥ex) ~Vj6"Jtr(\ol, MJ-R6flJ d~mh~ h060L bshamj~:1(O, sllLOlJ6 .plCXo)-::::Q. dJiJn~: f) 0)".] -til eXo) ~O 1 Xo anon3':2(lnL b'Jh19o(nJ, 1.1 (1l':J til L~o) <0., ~ aJjlJnac:1a,.~ bJ~l1n((lJ, 3) O\'J til (0C0) -::: 0 ) ~~J~~ W:1~~m ~jac1\b3j3j 7 _ e sa 19pf) £Yj ~d. 4) a3f1\n~ I\l\OO osMmJ~~KnL. 6J61Jq,(tI3hJ~L dscnm t'1('L,).:dirn .f'(Ic)--f(Xc) QIl Q( p I( ) x~:r" X-To if)hm~nO\ T C:ro)">o eJ j C~o}=o· s.3nl1rna Ilm:1: ~ :> 0", lllC'3hnL :lhDl-.1hOlt' e. ?loW 1111, X~Xo X-~o I( dKnm OJh~~~"hL ~ O!lhf9ncoL oLJ<nn a"eJ3m, ~mJ3~nu' ~ ~l.j6'fltnJL :Jffl~J ~lrlY" X-~o {1~n:,:1 bl\'(JJ6\'), hJlJ' anL lbt"?JJ~L.. ~. o· ~ /' 0 . J2<1U/m(J .;J a()eJdfl\~n ~ lC~) (!J X-Xo x,-:k, ~MlG'jnhafl~6(hl6'~¢n Cld6'~jo(\J6· 2JI(}.jl,Jes(1~ ~ICX) <. 0 ) hlT\lYJ X <,'~ eJ 1 ~I(X)) 0 '~O'\U'J X/Xo. OtlGJ cnjrt\h~dflL mJ6Jbare 8J~rt6' ~ b'Jh~n~n lex; ~~6:to'f\Jl :l:f6'jOO a"6nJ~an. iJ a&~Olte~~j JhJ«(l\Do'tlhse Jb (-~(X.)) '3tl,i6jU'nf1L os6"bnc{)nCil eJ i)-(\~ ~J3ntfJ{)jOf)t1l. 3 J GJOflcnL e.5W2~~f)trJ~(Je UJ1dJhllUb am~I\~~J6'ma\ Luaf) ~l.Jo')(\ ':!~6'.tIrn{)L 8J6Jenm" I hl'l)6 UJd(\~3 ~J6alb3.3?,.J'd(\ -?" [:)Co) = a, aJOn.ld jnM dJQlM6nL0I3nL ~ n.~mL an onJ~aoL ~NJ>(\(n ~2",kllAJ\~nL- 3J:t~na~anl- ') bmcm d~wa~LOl~nL ~n - shu' ao6n2~af)lJ ".1 JhJt dJ1LO 1 a~anl,·sJ.,'~n ~~6"~ltM~nJ~ ~CX)=X4, ~(X):-J:l.(l +(X)-::X.~ (Xo-:::'O)· .1dm!Jl6~H"c(l\~.). h.rn1~ ~~jC~eq,j 15s~aCtUMel\ ~Oj6':llJ'nm .. 2>hsjo~G tJs &I31l0lm6' "~~6'-jl1'''J~J If sJmetl6"j:!r.cn 3of"e:l&,H71 , (JVJ ~h~~l\jnL bJ6 nu 1\1" ~jhtfu~T\ 21J?l(:J6':1(() 3bJ~n J ej ~.{"jm7>L ohJ ~MnL ~f llm<n. ~A6'jd"cmS.)"' hSo3J ~c:1S(je<bj B"Jhd",~~Je(l ~l.lj6-:fItf)n1J ohJ~o:)L es 0l3()~Jn6" ~'-J6:f1YC\JLJtf' .,Ub6~jnC() :ll)me~OJ(7)" ~~ ~o~t;/\~L 6'j6oL3t)Jn Ojh~t)~n aJ3(:J~{Jcn abjJn 2eJ~sh.1l'!\M. 6~~n:JnL -:l~~am01' , ' 'j4/ " 0 -/-j~j-aPl-(b"""'6-3-:Jn-c-n-~ x >X" is oseS(!'~b~()L 6~hdncn. O.sh.am3~Jen ~"J6'1ciML ohJ~n~{)L o:lhlSoct- o.1e.:H!\~'?lOL fr.:l~c9ncn ~b(\'H?:l1.\ ., ~'j s.J e:~c9ndbj a~~fIld" ah.>~MOL J.a(hlb6'jjOd7l~.) ()lJ'3'J'-J -RJ~:fr\aninL'" Jb Jrihnjl\Ol. ~~~~ u'b j en.h hmJ 3Je.H~':H;-?HH.. f)jh19oCbJ OJ?>cnl.JlJ '316ja'ML ohj~l\~() 2lJeJCOl., ahJ~o[.. :JNrlfI (lOJhM?J6 J.imh~n. IJ) 3mh:1 d J. ~<l1:!'b.)(n, i'(X) hS()a:l ~':lJCJ~~ bSkaOl.13Jef' ~~6'ju'()')J. Jd ~1~UcJeibj: {) fCX) .52m~6'jlnc().) &'J06 e,) 2bmcme £lJ'do6, hmdJ i?'CX') shJ~heJ~()J' 2) fC:t) R,1etJ6.'lfncnJ 8J~(\6e.) 2ofr1(roe.8..1''£ln6')hmo'J -?JCX) tShBcJ~Se()J. e.Jd£5l~f\rr'j~0. f) lfo~sLb.sh 6J'£3jt;'0'\0'), hrnd hS112:l '11~SCl e"hj IlshamJueli 03~16:tU(\J Jamlb6'j jr\Cfu dJ'}ln6 e~ 2hmane .asaoE;, hmlJ'J s2 'd~JCJe()L.. 6'.:l~nl1d():lhf\ m~n X eJ )::0 ~,JhL9nCl'lLo13nL u~c e nJ 'J t9mcm~o -FCx; - ~(Xo) ~ fICXo)(X- Xo). (.n SdlilJJOl~I\l.. en~:lhrn(1l (~l -tCXo)) l)~hL9nc~~ 2lJdJ~JCn ab:J~(\L 606'&nc~oJ. ~nG'J~e.r6 db~ ~n .J~<ljQ1~Snl .. Sa 'fJh[fuc/b~ oS(3.s?lJC a'h~~/7lJ ~rn6'Jt;, Jd,,!Pm2 dl'L 6J6"r.9mClU jd6':J~ U.JU 'Y- ~CXo)= ~K(~:-XoJ· OJ}'<1mJo':lffiL a:J{l\a~(Sl"n~cn 'an6'JJhUieJ Ci.s'hlJen6'JM K~-?'C:x.c.). ::J.(1. ~-~~1= :: +1('ZCoJCX-~)· W'C\~J6JO' 'Y= ~1[Xo)(X-~)+-¥(Xo)· hs<?~J6J(f u2m~.(;:l;tn(T) ~f~J§'ju'nnl.J ~hJ~"~T\ ~ ':>hrn :f~~Gmo\JJ 1 ~n ehj ab3~n '1 Jdnc.901d :f? (x) ~:J, Jh~ f (x) ~f'I(Xo) ('1:-3:0) +f{TD~ J:tJe.s6 011" 3C'Jb':a((f1SOi C n lSll\crn~L. ,j") t!jh es~dO'-joU'O\O\~ hroCl l1\~ ~c.x) ..sdrnct6'JJn((\j, (L'dn~ -rlCX-J Jh./bf\ e"r.nJ. JdoW()30L 6sS~b(\CO\O'\ dO\(fjdOJcn 'Q':lSOeOL 6"'J6nWn:l~n Xi. <:X2. bJh~nej2,f1 eJ 3j~3J5mOJ, hr'13 f'(xU-'i'. 7/ +ICX2.J. Ol~ C n 19rranoJ~n X -nL nrl\c'dn .l~liC'.1~01 X.L -L 1 ~ -nl. hrn('~n ~n XJ.,-l" In?Jf'\C''~~011 ~O\d -t{X,)-.f(I):2.)~ f I «;:cz.)CX I -X2.)' UJ()~J6JtJ) (J)'1 aJ~n013Jc\UI'n6:l~GJ'h(hJ XI -':(2,(0 ' C:JJ;t6.1~u (2 ) 01'j C 1) c2O\cfl16J'dn S~H\(~'.~OO1 Jnhl\JfHn; - X-elL hrn~n 'X 2 -~ ~ ~-ri i-f!'C''?n ~() ~i-- U I dn~(\C'~~(J1, hrnJ -t:CX::LJ- +(X.i.l ~ -ttC'::c~) (:x~-Xd. uS(l~J6Aj f('X 2 !- ¥(Xd ~ fCXi.) . (::,) '.1::z.-JCi (2') es (~) ~()lm(m~J~n~ll(i aSdlha~fI(iJ~;)Ol~L.. 7 hrna + lex i) .// ~ I(XzJ. ~ '} Jb(o 3JR~~60\0'I jon/dna-., ~-{). ~J-R~~6"'0I 1 hOld Ol~ -t'Lt;:) .rUbh~JenJ7 2J~n6 -P(t;)c.) sJrnCOG:J..mCl'\J. Jdnl.JOl~nl.. [;J'~JJMLn.) eJ,?>Jc1~flu'fr\OI (i). (!l1JfjhJ6iloL O1.1mhJ4nL (J)JtJJb8Je X eJ Xc {)Jk[jlnO~L 'd~hl'L ()61-W~~~l- ",uOH\ C ~()h(fu(fl,hln2 tC-::eJ-+CXo);;:; -F1Cc..)(~C-~). ~Cl\[JJX:<'Xo 1 2/iln6' C~Xo es -P/CXJ-nL silJCb~eJernSl'1L ~J;)m .pICc.)~/-?tcXo). h"e21J<l Sd 'dJdO\b3~3J'df' x- Xc <. 0, arnnC!'J~01 ., hrn.1 -fICC,)CX-X<J ~ _~IC~)CX-X,). Sdf\!9O\J -tL'X. j - -?[~) ~ -tIC~) Cx.- Xo). J. n. Jd '<l:JdOlb3gJ<jn L1") !Jsdsh01Cn,16nJ. t\!I\tr's :C)Xc 1 Jidnli L)~ es ~ICC) ~~ICXo). ~\)GJn~"{\ JJ~Je X-<J:/D, f 01f . JdnL9md 1~(J~ an3nC'J~01 ~ Cc.)CX-:x::o) ~ +- LXo)CX-J:oj VJOJrncrndJL. usnt:J6.J['/ e J 3">1.!.>300C71, hrnd C iJ Jd 1rJhJeJ[j' l>JdS!\()) ([)joflJ 21 dLY11\u'€:l~ sosarro()"JhJ ~ J 0 (- ~(:rJ J OJUj<lfu'nnL Mobil do tn e.f (1) -fll, 6J?om~~5jD(){)l. 1 esJtS'~f\tfj~~cn U1:ltllh:JdneJa es ~6';tu'noL dCl\6l"nt9m6'l1hmSnL J()hrn~~~n&.JS" 'j,(}~Sane· aSdrT)dlPODS h~rn6l., Nnd l.JJds~O\cnJ6'C\~ .st,I\~?lj 'a:Jae~~n m J m h J a j. 3(Y)~?:l,,(h -?Cx) hsn2j 'd%fOeC03 mhj'lh ~Jfl3mJ~£f\ ~J5"dlif)jJ' .sJ ~JC'"'J~~.'J; 1 iJ -PCX-) Jdmills:JofnOlJ aJ'dn6' eJ ab01cme llJ'i1nEi 1 hmdJ f'''('X,) ~o , .2J ~CXJ RA6~~ aJ~6' e.~ 80mcme Yan6', hmu'J .p"[X-)//O. 14 <n3mh:l3J· O')~ (~, ¥(Xo)) -rht\L hSil3:1 ~~sC;Jetb~ g'~2m36Jen -\loo o;~6'jdnnL Ohj~MnL 2lSeJQI"6!>t\1. tS~hl9C\cn a~n6' -¥IICXo) ~ sh sl\l.j~miL. ,0$(; ..p1l(Xo) :.0. eSac9jfllY~. 300~cnUJaMO'l 1 &a.sc::nmJe, hm3 XO -nL d.shLib6'n '3 .p eX) .rjll\'~j.tncflJ 1 ash~~SO~ ~n -Ri66'.1:fnC"t. c3J2l\6' ,~-nL (lj'hd~6n3 -F1(:x:) (1~~J SJu~hl!~O dJht36'03 l ~n - sh.J~c~$J~. Jan~d f/Cx.) ~ .f'Ca:,) 1 hn\lt" X <: Xo eJ -¥((:cJ 7/ +"C~) 1 ntnu'J X7Xo· -0· ~3d(J ~:Ido\b3j ~J~n -r I [x) // .ftL~oJ # jL -1n oaJl 61l"36J;G, hrn~ Xo ~(l\51'Q -F'[X) 3~6'-1tJnr&. 8f\Oh~8i'L bJl&\(n. ~aJL O1j(l'lh~JnL d.sc..nm 2j).sLd35nGl~ hma .f?"(XD) Jti Jh JhLJ&n~l- '\ 06 -¥I~XOJ:::O. '2}JQ)'(}?>b' J. -P"CXo J =0 SML J':lu'fla~("l1 , dJ'"IuJ shJ LJs:l3JhfHf\ Si1i\m~J Ildr\l.JJOI3nL 1 hrn d Cio,¥-exo)) I\Jml- ~C2<) ~'16'JltnnL 6hJ~Mf\t, aJeJC'~tijnl 5JhLPnco· dJOJd)()1Je t6<J::X~ 1 ~"J~:h)'nnlOi3nl .~11 Co J:::O dJ~hJd ud ~6'jmmL ahJ3n.1 L 3S'~JC"'JG3f\l" t'n c9oCf\ s~ (3Jl~6nJ I nSeZlJ6" 1 C)2)(\ -Rfh6'.1j{1(flJ d(1J.1C!J 0lJ311L M6'LJb(!,jl\r\G .ThJ~n. ~~SC''(l6:lnL {)JI\lS!\cnL, sht.j~ll\~0L. lJ.r1dJr-nG j(\t\mnJL. (ldeBJ "dJunn m~mh'jaJ. M .p"C:t.)-lJ Xo-C\l- Ub~JeJUb~j abJhJL l.Jb~JeJUl~ @1~",6Y) JJ~~,aJ~f\() [';Xo 1 ¥-(';):o)) shnL ¥ LX.) ~U]€tu'f)nlJ ahJ~n?nL 6seJ"(rP]~nL oJn[nc(l. Jl. 01.i""h~2J ':1~':IS(f'\e 34c1mae(\6'J~jmh aseSM~30L h'Jh6'nCflL al.l61dhC"3hni;~Al t..J .rdO\~6'j ;1nCffi6J·· RJ~~J1ncm~nL 'a~wh~3 ~~arn6\~Jadl~f\(jj,~(n (bfl\t\j OlJrnh.iJneJ~. ~c:f\1jo'rtl'\lJ l>hS~O~n1J .rtnc1jcfO\£9J~n. Sltnajc9m!:9Q- ~ hh~~~ j~m~~J ~(X) ~~6':hJnnt, ~hJ~n~f)t. S1JoC'lJ'&(T\rJf1 ] ~~ ds6dOCn ~-l1L 6n.3en6'J~J Q.1hl9nmes6 -¥CX,)-<i ohJ~MJUJ ~WlJI':1crn~ dtfnr.eJ~J, MIYJ JL. b'~~cn IIjWLh':lcm~ ~ rnf\~j~S .:Xncl\hen~J!9alJ W()1) 3~!J sh(,~~h Olhn usb"!. sLoJj6'0\t90: 3~~&n~~,,() es eSbhncn. 3Jh(9n~J~M sLnj]d1'rI($hv ~:=.Q.., lJJ'bll.!-(i'hS1, Ol'j L.h'JCe3~.) ~r.l1'n 2.Jn6o' ~Ja~j6(\ {jlftIcm~JI1\J.3JDn: lim ~c..:x:)-=c.ol :)::-')0..- IIIn ~c.x.; ~=- ro X 4 (1 CP5thnQ!.'O SlJI\(J.. hPmHhb 3.s5t:Prr~JdJL )~3L LubJ ':i == KX+~. g?JJGn Jr(b.:,snJ 3nJm3m01 K I3?J .g. 52 ~aQ)b~nJ~(\ oc. ...... - (f:.) .ro x.'-"-t' 00. (}L~j(fl\~J rnM~~ ~aO'llBn<.J'2J(\ d~(Un~nJ, S-dr\t9ma 6S~~.f)tnCl'l\0'I ahO\-=l~O\(\, dS6SC'n01J e x..~ +' CO . -- gc> 3J!JL, 15 mhfl IdCJEflU ~:!.6jUflJ mlln IJ'.3cJeJJ/.; '!3::;!i:!tYflJ - 9':JMJJtl.)/';, nmJmt EJIJLu£{!'3hnlJ .Jh.Jj bndj)/£'.niJ DJll!PIJCflU hJn.1,J fJndlv3c..J. mAn u.3cJenb '!£Y£.11l't1.J .Jbtne.:iaJ. f?J.J,,;) dJ£3IJ!Jnc.JJ(J) mM U'.3CJYJil !i.J(Je3/JC '9':J5:jL!'f):ii6. Jon· nL'..J(J) f9':f&Jfl'fli?t, 11l77dXdlJ //'Xnc:iCJI1fJ JhJJ 5JdeJtX: hnutJ3Q}J /;/lJh.J3CJ. ur.:t e;li'lJ./I)(!'J!Jnb Jhn!J .h~ = JUx, Y) C'JhtfnciJ J. ~'.'J5.1Lr'nJ 'YLiJJ.J!J.fd1.J z: !Jnd!J3/';. oJd/J5 !!'.J!J.J6 Z~£().t), ,J!i 2= :!f.x,y). Df)o/)'lfj:Jfu 1iJ1Jd.J D,Jh!fncnu dne.Jdm JDme :J3.) b.JCJn!JdnJIJ (!'n.J b!J.J/.;, !JmtlJLf7l1' JJ bJ!JI!hd./ CJ.Jf)I/J 3 IJ . OJ'.:! Flu)/.; !>J(!I)YLnJ J, IJ'Jo.tf1J1) :}f} -.J£ ;;'.;!)/P/J01 2.;/.; JJ tf'.J!JJ!1/}(IJ[ ii-dfJC'JJm J.i3nJ. ,/fJ;),J3c:Jb JtS!JJ eJdJ C'IJ), (J)'Y JJ .ufl,}IJ.;JC/J!.J .!Im3.JC/J DJIJffflC/JLtn.Jnb .:IJ£JJmJb dflun fltJOJ/J dflBJdf!) J !Jmd.Jcf]/1 d{/)OlJbJC' ~'C'('llu ';d /.;/)JiJXJdfJ - t3.JD iJ.J,{3n!JI'L.J3OJ m,~n Ir.Jc.JC'fl/.; n!Um '!J::J£:IPfJ. ?JL, },/lk7J{lJlJ 2.J5uJ?J(!'30nu .JJu:X3/J (!'/J.J bn J )uJC.J :JdnJ . mlln L!'3CJen!.J '!3':J£.1I1M/.; 2/ut!:JMn. OXY-l. dJ)un:J'.YmO.J jm/llht?flliJdtn.J /';nbt!'J(Ud() IJI131vfniJ !J3:JO nJ fx,Y,2) o.JMf'nctrJ.J bnd/u3c.JIJ' IJmd:JClJ1J~3I)uJd 2=.:!rx,y) , JlJmC::JdJ :!fX,YJ mnfl Jf.3cSt'fI,!; OJ':J5:!1It>n!J{jld3nj/Jo mhn ff3C5enb ":J:JE:lJmf)U 2nJ~n:j() WIklm.rt?2:J/j'b LJflYJff.J~fJ fJuJ07 fJ.H!JJrYJ/; , },mdx/';.)LJ' C? C'Jhdfl!.J jJhJ CJ c':J!Jn IJ.Jdn!.JdnJhll !JIJ '?3.J .J!)J':kl.J!P.J!J .Jh07 D.J!Jl!hCPJ/J ;}3.JOlU· mnfJ Il'XJeM OJ'::J!i.1tfnn/.; 'bf:'3jJy). JddmCJ:J£, 17m;} A .;!Jf)/'; l =J rAt) mhIJ //)ot!fJ/.; PJ':!l'.JI/f){Jj, 'bf'JJl!fJ JA 0 bJhlfndJf1 eJ IJ)I7:J/j lim JIM):: A , {))'J J.fIi,!;.;Zt!'J!J/J!., JlllliJ OJhIN07J Mo - jJD j!J:JdJ('fJ £'.7Jflu(JflJ!Jn (.Mnl J.1.~.,M..D (Mn :t:)io) :!nJe:J3htnJnilJ013flL (j(Mn)) JndeJ3hmoJ :J!JJJJenJ A-iJE. 'JJJbfl'JEmm, IJm) r J!1.-Il) Jflc7C'J3JvndfJ!J jliJd.r6lrnOJ Mo o.JlitfhcniJ3,J!J £n2bJ3/.; fJdJU] hm} limlJ1,n.MJ=D) II 11"'1OQ /;JDiJ /JrtnJtoJ JM!.J J.J&!fI(.-fl dVn ~.J .Mo DJIi!fIJOdu :Jtn!JIJIJ, ..d'!J:JCfI (!JbJdrb17l1'.:iJxn J!J.JJf !1m3 '!Je3nf)!.J J,!;Jtnfl 3JCdJhtfJJd.J lff!)CC!3J!JflJ ~JJeJaf)L: A h()//!J3IJ .s!Jn/.; :l =.f (.h-~) '!J'::JlJ:JJf()nL f!Jf'3Jhn uUo bJIJ/PfJc'J.n, (J)':J 6JdnMn:;!Y1 £.;>(J IJfI/J'b3nWlJi3nb drnnJJMJd.! fI",Jtnf) !i:/t) !Jnlj' 03fl ] hmJ I j(,M) - A 1-< £. 1 /Jf!)tJJ {} <: / M..Mo / < d' j6:;, o.;(JCflCf) bJofJ07 l!fx,Y)-AI<.z, hmLt'J 0< !fX-Xo)J,,-(Y_Yo)2 <;)0 Jt:c,Y) q}'jE.1J.fflfJf., !be'35!Jn (Xo,Yo) b.JlJtlhc~ Jf!.Y)5f)'jOJd.J Jj,.J1J' //m.f(:J:]Y). mAn ,1'3C:XJ)!.Jt?3':1b.:! ::c -1 Xc t/r):iDnWl3nwli fJ.JJ.hJICflJ!)/lJ (J}Jmlu:J.Jdfl 1,);/1£, 5.JJhJ3(/)£ eJ dJ~Jhei31)/; 9JC7' 3!J.i?Y1l./ ---} 'Y" 2J!.J..Jt6..Jd . rnfJn IL"C.V5V7£ CflMifnflt -'J5'..'Jl,tJlma.J· 2::: frx, ')) tlj':J/i.1Jf()JiJ JDrr>e:JdJ ':J5'J.3.J!fn (.TO] Yo) D.J!lL!hC'(Jn '/lJ'J ,).J b.JhJlhcOfl .JNJ.Jam3L 4fl/.;n ~k'..J.JM <Q.) jim :!-IX, y) = flTD ,Yo). r .... xo ~ ~ ~() mhfl lJ'3C:5C'fll, o:J':JIl:flT'nJOnl :J:JJOJb~J3J2YJLJ' :7o'y3JIf£fl .J!lf)Jb '::JD:t3JtP '!J':'J!i:lI/'f)J(Tl.) j,;dfJ' !J,xlh.J3C? (J.J (J)') d-/.JiJ'J 3:5.kn a~3.ftW..J 6'Xilb.kJ.5fJ - dJ~JIJe:iJJ//' mhn if 3c J&I)!, 03'::JIJ.iL!flnO J.Jndrn f)'JA:]mi1'::Jo;)n B.l M'Jcn ,::nOJ.J1,7;;/~IJ.J0 ,_ '-~-n: .,.~ __ ~-,..:-.~ . .:...-..: .::z=~_', .. ...;.:-=..::::..:....~ .. -~-.--".~=----~';'- -=-=--' :In!J?J.Jc:n ))nc,()u jJhdm li'Jhdmfd":!c:Jdf) .75m e Jd.J lim J(X~ Y+Ll-y)-J(X,'Y) A')-" 0 L'. Y df(x,y) ()2 I -11 eJ na() J{!'Il[;r,'dO:Jd.J JI>m-.JhOVl 2JaC''Jan iJn:Janc:mm(): fy(x)'Y), C)~ .J5,dm!x':]<'?' Ly' ~y . a.J~JWe.Jd:J, :Jhm-:;!J(J)/l lf3cseno7 aJbJhJm.Jdw.J!J dJtnN ff3C.Jen eJ':Jn9MfuJ'!Jcf).) (!J .)Of)fl'md ~ d.J1l'.JA :Jm,72JII!.u!.J /lJb "JDO 3':J!J::;hmm hrn2mhlJ' ;}::;e0'tl3b· d.JC':.JCf) hnano 3:JIJdm DJh3rrLibc:13n. J::: (x,y) (!J J~ (T, 'J) tJ},'j&jU'fl.Jdnu j:;hdm S.JN}rrL'0.'::JCJdL :;t'me:J 0,) fix. y) '9'.:!o:luhnfJ JJrnN !Jf]Jnu jJhdm 6:JMrn.Jd':JcJdfl· J·n· d.Jmf..J /J!taIJL j.:;hdm DJf,JI'rl:J2'j E Jdr, .JAn.!;;: iG 'l-JI 'I' -::If' ;;)fl II 1/ "r" d~f 'CJ:},J {f2f 2/J-J ~J ~] 0.:i, -y. nWn .JI!Yi&!'Ja::iYJ..J6, 'J:;!.JJd;JflWe, Jb,;::. fx:x:' :IX'}, J-y:r-':Iyy , .JO oJtJ: -,--,--,-- OX (;':1 oJ: (J~ dX'< CJ~ oY8:k ay~ (If f,1 J X'J eJ 'YX: J!ime.JdJ/h ,JJm!l.J lJf];jnt 'JJ:; h J OJ C 11 3JIJ1m 1i'.J/);:]I1lJ'2J':Jc.JdfJ. ;/J!ljnlle.:Jd.J, lim;) !Jf/7/J:J n/.nf)n 'Jb'.JJ.Jilh 9:JfdJJtJ.J0rJ.J' d.J~nfj .JMkJ.JIi.JtfVJ!.J 1Iincfjf) JMJE !J.JZ!naJeJnl?, IJ-:JM hnal1lJ »h,Jm 5Jh2mWc0J t3J6n1J./!;(!'3h:itJ.:£ ~ (/J-/) MM/.., jJMm 5JliJmJd':'JdJn/'" :iJh:fn OJhJIYlJ(J:Jo(3r). M'Jcn @)t.!lJ!JJlJJlflJC1. t7J,;) l:=:!(X,Y) Vj':JFdlfnfll jnhJ.J01 IltJMf.., j.J1xIrn /J'Jhdlll.Jd'::Jci311 !J.md.J O'.JNfnc'dn jhnJO ::JiJ:J3.Jtf&1, doJd()O dlbnLfe:idJ,hmJ JJ IJ'.JMflc1J11 "3':JO:JdnN.! Mljcn r;J~efl LJl=:j(X+L!x,J+&)-:!(x,y) bY1JmlJeaM:;3.J iJ.J(y¥)7 L1:z? -= 9 f ..0.Z + g~ .1)) +<¥ . ..:1 X -4- p. .<1),] weJt! q -:,D , f ~O 7 hm!f..J .i1x -Kl,LI'Y..yD. -aX df df JdJe.JD JJdrnJenDJ!lJnidiJ, ,1m3 ~,:!!Ij:llYnnu LIl':/CfI 6"./lht!/J& d01J3J!ln 1J.JlJrx:.flJ dX f:..T +-dY L,-Y. J.J/'" oy;£j !/nnb ULlcn e/1'5:J!J:JEiu'nxn Jff'm(3XJJ BJ nJn dJ(X,Y) uEj d:2 UnddtnanOJfJ .1c'!l£I1Clljit3.;. 07::1 dJ.3fJbL.J/i.it3(7)]hrnd BJJrn:Jj()eJCJ.JcfI JIJC3':Jd.JSlPn/'" DJ?Jhen ':leAn/" .7/J/'" t:M:1YlJD'L!hJcL;, J·n. LJx=dx 8'-' L1Y =dY, dIJJf)(-::.JJ(J7 dz ':: (Jf dx + @.Ld') ax 3Y mlln !l"3CJ<:Il0 hOJ!YcfI '!3':1fj::!u'f)()L :J2hdm EJ.JhJm:JtJ!Yc.i3n- tJi':J 2=:f(lL,V) [JJ&Lf LL~1/(:x:,y) (.J v-=R(x,'Y), dJ'dnf) d2 _ ol au {)2 (jv di!. _ (j; CYU ()Z av oX - au . i):r 4- aV - 3X' a-y - fYu' CJ'J + avo 'dY . mhn !J'3cJ en/'" f!3'!JEJd linn/) :;diJrflJ.Jd'.JJ() :;dLI:!JLJ.d':i:Jn. (To 'Yo) !lJIufncf.., Jbine.Jd.J l=f(x,y) '!3')J::!unllh d.;.:!Ln:J:JdIJL (dnlind:'JdnL) D:iJlftXTJ] (m .Jhf,:k3ffJ iJ Jd b:Jh!:fhdlb nlJl1Jn dMJJm, Ivnda>L 5m3-xll (x, y) D'JIlt!hcnLtJ13rJlJ iJh':Jce.J2J 'jlP/llUl"J.J j (X,Y) ~ J (:Io J Yo) OfT]')) >/ ffh ,Ye)). f):;IJIfnc:LJ .J5rne.:iJ.) mhiJ lJ']CJ(!;)u u:Y:Jli:JUhnL .Jj!JJfll:;(}~nL 8:JMfxJ7 l OJ'.J nan .J!vlL, Jd 'S':J&JLmnL J6 aJ:lund~llu J5 d(JonJ~Jnu 6".JAt:fncn. 9':J&!1Jfln!J J&1'd-3oxnkJibL J:I!.J1PI>Jd':Y:JfJU b:;htPncJ2'Jfl "3':Jll:f1J'M'.J .J:l61ff'l.J:J':Yi!:JJrJ j d3n.Jcn . m/)n IYJc;enu '2><:JE:JJJ'f)f)/; J.1L;tf1'J::;(}!::JdflLJ JilL/oman/'" J ':J 1Y n C .J a.J c jtWr0.J6u fJd":;3.J '(JJde J~n ()JJMJd.J, (J}<:J rnhn 1J'3CJeflu CTJ':JlJdnrlJf.., liJfkJ.J 1i'.:J!vffk '(]() x!Ju :;.iL,f'l1J(bJn] u.J CJAf Jc7 D'·)/!fJn<:.'Jn Qjj;;:/ lthriJ mnfTlfl).J'YcfI j:;!-Jdrn 5'.Jh:JmJ3::JC1l .Jfj /J':JcnL IfmdlJ t .10 J!l ,rM.Jdm2LJ. f.'J;}JPjnl1'.Jl3.J. mhll3J jJhdm S'Jh:JmJr,':JcIJLmJfl1.; :JM:;l!mooJ JhtT!5Jn/)nJ, JJnJ!1nJ fI.J3Jt?Jhmm I13f1 JAm -JNnnL.tJ6flb. I 3.J!f3JSmm dJaJ07tJlJe, hmJ P7'J (L, 'fo) bJlJJfhm Jlint 2= f.CX1Y) ~':JlJjLl'fJlJ1J J.:IbJ:i¥J:J;;~.JnL, b""JhlfhC/J, dJJno -f.:iToJ~o) JE E!J(J)u tffncnJ, .J1i J!J JlJlJJ3tn'2JiJ· 3na'JCfJU!:x1/TltJJ, aJ2'JJcnmJe, hmJ (x." Yo) JJ1tnJ~;}1lU lDhJfnCflJ. dJ 'J 116 nJh/;j?JaiJ JJ QJ/Jl/tJcnL ntJdlf, 2M.);}//?, hmJc!1L Jm32dl (X, y) DJhiPnC!JLm3n.u d.Jlj,')c~:JC3.J 1(X, '1) ~ f (X 0' Yo) 'JJtmcm'dJ' 3m.f3.)(J) , JJ :J1Je.xJmf.., hJen'.JLJn.) S. 2Jb3nblJOrr'11 Jd JfJC'.J2mL imhnfbrn!J!lJC2/)n t?()J:J.21f'1JrJ. jd e().Ja.1'tf;'~.J JefdJ/):J 5'JlllPnd"6L .;13m b.JIJ.J Ix ;Yc,] , bJt?.Jl!' X {-. (XD-~' XD+a) . 1J'o.;t!nJ, JCr;I1'Jli"lCfl 'Yl!hJcm<J-J 'J.:;ooce JdJ .Jd bJh!ffJcfonu(JJ3nwU', :J·n· f{x,Yo) ~ f[XlJ,Y.), hmU'.J X6[X,,-J1Xa+;i). .5t!!3/jfl~&naJ: !(X,Y,,)='-f(2:,). dJ'Jnli" 'f(X) :5. '-f{L J, hmlJ'J Xl: (Xc-d) Xet'f)) . Ju :In nd.JiJ 6n~IiJ3L, hmJ XD !:fm'!3f)CJ .JhtJ)/) IfI3c 51!?/lL ,f(X) '!!J'!J&:f/J'fY!t JJj unJ':J:JnL bJhtf'J1c n :JA3fJIJ, '!3.Jh3.JL {f}J!MJJnL (f).)O.JlJJ.1(3, ..plrxo) Jb Q':tC/lt tfJrrK:nJ, J£ .Jh :/Jt.J0rri3/..,. J.13AJd '("(Xo)::. lim 'f(X<,t-L1X)-'f(xo):::: lim f(XD~·AX,"Yo)-f(:Xo,')o) ==-f.:'t (:):0)'10)' LlX-..Q L1 X LlX~() Ll X ,l,JnrlinJ J';'(Xo ,Yo) J6nJm3J .Jli [j~Cf)J, Jli Jh JliLi3IT1J/.;· trr;;mlu,]..; CJJtf:5nif:i2J"lcnJ. mnn lJ'3CSeJJ0 "3~&JlmnU 2i/.;tf!AJd'2JnL JMf2Jm"Jnu uJ!Jd.J/)niJ JnIlmaJau nd03J 'dJdc>.J2,fJ (J?]mn :Jd,J. 3(]):}3J(Jl, [XD' Yo) 5Jn.l/'n&n Z = J(x, Y) OJ ')/JjifrIJ[; r'3.JJIi;;n.) lJ:!Jcn.u d'mc/l jn!J3~'CIJ IJnallL jJl.Jrn 6Jhd''1J3''1cJon eJ '1EJ'J3JtPn J:JmhJ hnC3nL jJldm 5'.A7m.f2J,ciJn. 3tfJf3.J01' A = f!:::x (Xo l ':fa), !3::- J::,:/ (Yo] Yo) eJ C =. f;~ (Xo,'Yo)' J/Jn6: 11 (J)') A C-B 2 > 0, '!3'YS'fU'nJu [Xo J Yo) IJ'.Jn!:fnc'dn J13LJ J.1IJt!hJ;hJn , u.JbJcernoh - dfJ!)flJ~".Jn , hmL!'.J A,;:>O t'J dJd1.lldJJI1 , limtrJ A <.0 21 OJ'J AC-B 2 .(o 1 ':3~£jL!'n.JL (XD''),,) bJhtfnc2n .J11Jt!/).1d':JJfJ Jh J13!.J· ?J) m'J A C- 1:,2= 0 , 03J:f3t iJ.J.J"if 3m 'dJd91D~3.J' .J·n: '!:J:J5:!U'().)/.; 'd:;ndc:;o.) jdmlie:;L ;}gILrtlJ:JJ fl ; ;}JndcJcJ.J JtlmlieJL dflonJ::Jdn, Cbrw/OdJ .Jh j:lrnlie:Ju 2:!btPlvd::t:JfI· tb3.Je5!Jt0J bJJnawJonlJ aJom:J3CJ?JnwLJ bClrv'ue dfJ3etJ3Jhcn 'dJoeJa JJmlt'.JD.JJeJ: dfTil/Jd::JCfI :X:JUJ0 S~DjiJ[).:k31J ~rnhniJ 3f1Jm3lTl31 nJ., OJ,)lJ:ji}1JJ, hrndCTi/.;m3n!JJL/ J'!llfJd:!C IJ.JhtfJx:.:i3[)n JO '3'-JDjll'f)nIJ J[;n'd3o.Jor;}J 3nC'..5fJ 5'no.JfJtJA JmIt:.Jc?'::Jcn ;:}j!JjJ.fl<:JJ uM!ne.:u3niJ cJJt:.JM:k3nLJ :J3Jek r lfY3n!J 3JJfJ .JhniJ :YdLl'tYvun . .3JbJrtDnCfJlG ) JJ2JJ(()(I}JC:, JuJ{))/I Jdmlr'JbJ: dJJfl:J3JomOJ IJlJlnf);/6mJJ&) .oSJ nf;..'} , /)me? !Jrnlf..J 2'Ycn ufTif!)c.iJneJo .JJ J SJJ('] c7J5df)OdnIJ )JJ() n.'Jrnl ':JJ M0JUn . Lbj..)[j.Jf)~ hmd 301:/3JO? 7 iJn<3htP.2J9.JJ Jrrllu,ncn..) DJMh cJ3n: A1(T~7Y1),A2(X2.,Y'],)·-·,An(:xn,';)n) eo.J 2mntnDm.3.:K3.J, I1rnCJ .Y3.JCJ 5'h ~.JU 'Jm/Jnu 3n.Jr,!Jf7l 07 nu }(X) ::::{1x+!J O'IJUJ.J, nmdCI1!;t7l.Jn/..;JU' JJ&!fl.::fOf)/.; 3JJn n Ad)If-A282.+-···+An8n:::: LAxB K n:f6fJJ :Jdlmlulrl. )(=1. JdIJCfI 2J.J0dI?6J3fJJ, hf1,J dJod/)OdfJlJ JIJ ~JO'/) n:i- f) .JOJ :Yd L!'n!L7L;fI I !VlJ/f J ':JJ L!tVlJ/;/) n:!!J:idJ dJ(' JMJd nu itJ en ; nn EAxCx Jb:Y 5.kJfJ L j}txx)-Yxl )UJ[jJ(Je.?JnCJ k:.l X:.1 ' Lin, ~~hm iJlI7b:JIlbJI3'!JCnJ 3nlf173mm hmenl ndli.:i3J '!J3 o I> ( :< JlnhJ!Jn <l:kJe:Jon 5-'dn ~ E ftXx)-'jx) (Jme:J X=i CJ6neJ6 j35e/).;tP:JJ1J a5eJ~Y) JJJm1f3.J':JGJJ nJflOl' ImJ Y=):£/ o:J'J/):iithJ X==O OJhlfhc'Jn .;n.JJ /).J!>(kn..) oj en 7 h()f; oJ2mLJ' 'd:J2J:J.i:J5Jdfllt::?J o.Jh:HJ:Jcn !.JrJJJ(fI~GJJan). d.Jd.5U5Vd.J, IJ.Jomcmme. t3:J[;f.., bfl/J../JJ IiJdrn:JJCJJde j J.JJeJ,3fJ.J JmLi.Jb..J; 'JlieJ 3J7Jrn.3mOl fl/..; n [l eJ -b !WJ'D3Jdn 7 nrn(}JC(JlJOJ.Jn!JJiY F(a,-g);::; L. (!2Xx+g-yx):{" mAn ff3uefJ6 t:3'.:Jo.:!iYf),j ){-= :t cJ6'.Jcrn3/; ~difrkJfJ '?£"fI'J36JOrJd.JU. JJ Jdm!JJb17f; dJeJo,)J.JffJ jfJ JJhiPn3Jc: d.Jfldc:JdJ fI)/if) j;J3cJC'f)b c:.J':JEJj!J(){)!.J .JjlJtPh.JJ:JJn/"; JnIJrrJ.:;{)()/..; JJJm:J:£..."J;)(J). Jd!Jt!hJJ:JJflu JhlJ.:iJrrdit J';jLJ'f)C.JC:JCf) JIJ!VICn!.J dJLncn ()F{a,£) = 0 jja eF{(£,tJ - 0 of; -, ! n L.- 2 (aXK+--t-YK)'XX =0 )< = 1 n L 2 (aXK+b-'}k)·j = 0. A-=. 1 2 -~.J d.JjX'IJ'f)!.U c.) 6J3AJ3n!J L'.JCJ.JIJJemc: 3Je J 5 J':)'!3J{)fl6 (1JdC' JCJ b()UtP.J<3J df){}C' j{JL LUD.'lL, V::~;){l + (/:;XK)~ ~ l";XK'JK { (Ex"Ja+!J·!J=L'Yx. k-=f .-'::=1 h.J&iJo :J: (»)', \ X z 1')2)"', ::en) ':)/1 !Jnit'63.Jd() 2rnLY.Jd':JCf).) , dflC'.id'JCIJ &lLtP:XJJ (] ('.J -£ u_xffu3.JO) 'Ji,.JlJrn6.Jd()U d()d.J!>m o.JfKJmJC!!3.Jo!.- '!!d.JhtlIJJ:JL -mil :JU6mdfJ.JIJ 1J!Jt!3f13 ;!.J/)tfJmc;"JJ07.J /..;/)IJff.J;].JiJ , hm)C(I!J JJrn!J.LbfJOJ ]f)J)lTl3n:J7 a f!J .g -/..;. 17JniJ eJe236.J, hmJ b.JJm3bfJ ({l, tJ O.JA'frJCfl /J.!o.i].J F ({l, 6) CS'::,S:liJ'()n!.J dnO(),]::JdfJ6 O-Yl J!h en , Jd!vm.J.J .v, 6".5MmJe'dJM biYJtlJ':J'.Jl. jOh·Ylc~lY\~(lCn. -¥(X) '?>":lO":Htnou jnh3~C'jrn"nC(\ 'hsnd'J ':l~sc:lelb.? ~6m":J~J IlLjOl F[x) ~'j6'j v'0J1,., hmdCr1!hl?lnWll' Sd ~~SC:lefJL .J(t)~:JC b:lhl9n("(ln Lh~('a.J6s 19mcrn~J F'C::o:: .f!C~~J , Xi!l ') nJrr (1M~:lj 'I d F (x") -= f(x.)dx. d6:lCn esLse~:liif) SOJJ'l hmJ ~3Jc.s ",3'j6':t1J'nJ!" Sf) CSd~6nJ Sf1k:?K'Jl1'\"jIl((1 .j;)'J2fIW\ -f;~J6 eJ~e 0']6'(1)., hm~ (])~ ~':111;tLtnu ':l~~BJl9nJ ~ 2S'Cln6 a.rL oJJ~6nJ jnh3:Jc'jrnll.loCn. q,:Jfl)hj<'lj. tTl'=\ -¥-('X) (t)':l6:Jl1'nJLJ o~~RcnJ :JhUln a,SMU" jnh3~c'jl'\~(\(n Fer)., J6'dn6 aSL OJ~~60J ~Ja hJ3n 5(lh3Jc~mQjOCf1 os ':lm:lC as(7)?JJ6~ .rhL LJJb~ ~(~n= H.:x:}+C, weJlY C 6"JOnLJdnJhn d~~an3nJ. esdO'~nLYj~..\· c.t ('X)c:: F ex) t-(. I.JJbnL "1~6:ltt'oJtt hmJ fex) -{)L Jnh3:l('~rn~()(n n:l6J~J MJmden oJh:Jm~L O-:lnJ<>., hff\d (J':IellnjOL oIkJ(l1J~tJ(n o~CnL dmcru. a.rr.OlcJli 1 PI('X)-= (F('X}t-c) I :::FI('X)+C~ = t= I(ex) -= .vCx.). f ('X) Ci:i'j6'~LYnnL 61~nLan:Jh lnh 3'J('~m~n('L hlYl:) <j? [:):} -:::: F ('X)+C llJbJ .l:J2>u - Jo a.s(Jm&:n5Jh~mou o:lMSD, hmd O'l';j tlSn3:J ra':$sc~e'b3 1O"J6:hrnnL S'.rhafl\~~~Cn 6''jenL, t9mmJ' 8J"'206 J;t ra~sne'lJ ~ 03':j6';HroJ 2':1e3n'1nJ. 3skcnc.lu', hse~J6 (p(x)-Fexi)'= c£'('x)--\='exl==fCx)- tC:t).::.O'.sJn L5\n~ PL'):.) - F eX) = c, usoeJ6JO' <P('x.):::: H:rJ+ c.. 2lsc~LJsCbC"~hJcn n6C9:JOhJcn. .pCx) "3~6JtrrH1L ~~Q~ jok:;jC~fl1<7jncO')J LnahJ3CJL ~crnejbJ Ja ~~6":htnnL oS6'JIJ.f<bC'3h:Jcn OGGlJ~hJC(\ ~.f ncn JC'n6n':!6'~~J jhcn-3"mn ~.1J<?lan Lnibmcrn~n: ~ t J te'XJ 1 S -f(x)dx (OhD]3S1 hm3 ':1d'Jl9j[, ~jdcnb~J~j'Cln 'J~h('1 arnlJJb~hb~~YnJ ~j.sIi,\u~6:lC" J~6n~ 1 ~firtL. cSdmjJ6'3~J) , 8s2s1J.feJdJ J ·f(X) dx =- F (X) + C, l.JS6?J[I f=(x) shoG t-('Xl-nL :JnG\-::!NM S()~?lJdfTl~l\cn, C. jn - 6''J~nLJnJhn :3"'.Jean"6n. 1) (~ t ( 'X) d x)':: t (9C ) s 6' ~ d (l f (X-) d x ) ~ t (X) d 'X J 21 ~FI(X)dx-= F(x)+c 50J jdF(X)=F(::t)+C) j) j K t(x)d~:::K 1 Hx)dx ') bs-eSIi K 6J~nLJnJhn J~~(jn3nJ, L f1 j [t('X) + @ ex)] ct X. :: ~ t(x)dx + J ~ (~)ct~ i.) @j 2~ fl3nl'J~j~n 1.Lj~':js{me n~tPj'3hscn~ CS6L~("'3h:l~nes6' (;JJm.1"n6..rhJm j Jo 1 olTlcm ~) e J J-I J dsh f9')~e :l t9~nV'e~rv6 6shdm~1>'jC()[' 'lljbf6JdnLn 11l3fJL 'J~ nL ~JJm~:J6JMtn· 'it .rhC'1 cJ If) 3J'R?JJ6mg'l) dSO.5crmse) LJ) 613()WJ. 3CJ;}3J(f), FLX.) eJ G[X) .JhnJO 1 '3':ll.JJbJ3nwe 1 t(~) es g(-;:) ~':l6':hr()~'~nG r.Jnl.:l jnh~:J('<rn!n Q."~bn· JJ~n6 J tex)dX -:: F(x)-t C i eoJ 1 ~ CX) cb: ::: G (x) +(2 ' s:beSb Jt(X)ox+ l~('X)~X= (FCXh q(x)) +C 7 (i) I I ( oseJl;' C~C:{-t-C2.. ;}:Jfl1h:lL Jbh,,~, i1dnl oJJm 1 ~fr12 (Fb:)+GLtX")) -= FLX)+ GCX) =1 :- +C'XJ+~LX) u~ ,u-'il.rUl'f!SJJ lFCX)-t-GCx}) shnL L t(:x.j-tS(X)) c'l3":J6':hrnnL Jh(h-Jh01n .fnh :>3c~~~ocn , ~~(3~rtJLns es:.tfJhfTIm l[fCxh~('.lC)lo'X:: (F(x)-H1CXJ)-t c . (2) en (lJ (21 (9mcm'll:l~n~J() ~(!1:J~~C01~(h eS~sjtP!lOlYJaY LPmCrrlaJL. i9 t «. xo{+! \) ~x dx:.~+C (q*-1) )J dx :m tQ ':X:+c. W:x d, 2/ \dx = ~h \X\,. C J';:C :t) J ? x=-_ c.t~'l:+C Sln 2 X 3) \ a xd x = ~: + c g) r dx - m:csinx+C j eXctx ::: e X + c jji-~2' L}) J Cosx.dx:: SinT+C ~ dx -a.'l.csinT+C. ~)) J 5inx cb: =-(1)s:x:te J Ja 2 - x2-\ ~ ihuanl. bjhbn J'O~ 1Y3csealS oshes:f.16"nJ., ~lTlhJl>j(' J ') .,I \ Q)OfYlh:3J' ':)011?lSffi, ~(X) sho'u OUCl\n ~~6':Hr()J, hmdj(~Jli OJJRor\..l jnh3Jc~fYl~Ocf) 6t'1(m~6{\ 1 :x -= '1'(.f:.) hJI1Jjl'llljSCjecn~ b'J'h21n~bsen "L~cnn ~t:16':hrOJJ 1 nmdG1L J6,,~cm~JO'lJ lJnJhJ3d ~~ ,-/ t['X) ~~fV'nnl 6s6'USb(!l3hnIJ J~t"J:n ') as%'16' .f.(f(t))·f'(iJ' OjUj6}lfnJwIJ' Jt6'J,}J .fnh'3~(I13'ncn E's 'd:JI1IIJ~JSJ [frncM~J ~ rT' Jt(x)dx.= J ¥(f(±))'fIL-t)dt 1 ,h'\)J -lE 1 (i) eSdt5'~ntrJ6J, ~0'l'J3J(7)") Fex-) ShnL ·H~)-()L JhOl-,1hcnn jJ)h3']c~(1)'3ncn. :J·n· Fl[x.)=-¥(X). 2~f16" j.Hx)dX::.F(~)+('. (2) Sl!')5n'll6"rnm P(1:)~ F (f(t)). hiJ1'.'Jc.n O)':J6.1linnl> D.5b.5h3m:13nL SJlJnL (J)55JbaJe 1"CtJ=f=I(tfl{-D)'-P'(t)= = +' c ..p({,)) . ..p\t). ~·n· P(-t) .shnL f( fCt))·..pI{i::) ~Vj6':htnnL, 3hal-:Jh~1l Jnh31c~~()cn, SdnrPm~ Jt(f(-iJ)'f'(t)di:=epCt)+c, , (3) dSOOJd q:Ct) = F (--P(t))": F(x) . Js<an (z.)~.s ("3) L9mcmb~neu6 dr(3()('1:J$cn (1) lPm0n~JL (f)Jmh'JdJ' 3m13soh '11 ('jj e.s VC~) hSl"ld:J~~SCJf'<bj {)Jhdmj~~n 0LJcnn {ljOj6-}tlll'J6nJ, hThd 1l./(X)Vb:.1 O?!t.'J6":htnJL 3JJ-R6nJ :S()h"3')c~m~ncn, (If(lno Jnh3~m~fl(/) cJsMnJ 11 ('X:) V/C'XJ C?5'j6' :::hYnSlJJC.t' es S@21(1Cl'\ S-:l~u t.fmCmSJu j'U(~vl(x)dr -:::: 'UCXJVCX) - JU{C'X1VCX-ldx esa/9o:)f)trJ~J· os2h..s3cnl o..fb.rhdm~anL <:l:ll.flL tYlJ6.JbdJe ( '11CX) VC~I)J:= 'U IC'X)V( x) + uC~h/b:) , I t\C'X.1V I [:x:.j =t·u (XJy'(~::.)l- UlCX1V(X). tll(x)V(x) -lJ 2JJS~6nJ jnh~~C,jm~"cl) jnl\O'I~fll ~Jb3J<!, (UCX)V('X))' 03"J6:!1n)\lL Jha,-ahOln 3nh31C~0'I~n(n shnL 'llC'1:)vC:x:)., s3ntPo-l'J, fiOJeI\.l, jl)h~'Jc~m~ncn H6":16J Ub:h/ICx) ~t:16':JttnJ Us L1'. :1s'dn6' , Jj ;s6JL~~cn LPmcm~n L ~~3h -6'BhJ~ n6~~h~()0') dn3r1C'J6<n esL.Ja~f'\u'~v. 'Sf'r'lh<P.1cu lJ hmor11hlt 3mmcn", -tIC x')d X = cl +(X;"I .r2nl9m() ~J()L9j[)U'J~lJ(1) iSmrJJjCJ sl..,JLT 1"J~(lJ~J Rsnf(~rnL: r J 20 3S6lis<iJe3hdcfI nGl9lbhScn. 3cnhJl711 -FC'):.) JhrJIJ [a.,~ 1 u:lod:J6L?Qlj 3JG!JAO"?>h~cn I\Jfl1'9 ~~J6-Jttnj. ?Ji~nlJ{KmO\ b:lhlPnCJM'\ a:=. :c~..( x( z X 2<'. " ... CX:n-~'< X n-==-B S'J b'J:\{.Pn('J~r.01 dmrJj 3':JCf\ uJz,2'J6LFn eS()~m~.) n U'JC 3st.9Sh..\ vT03J61)lsP· 301hJ<n, :JIJ IJ:J2J'd:JGJ~5nJ , ':l:J/.;J~J2n1JJe) 1J i , /12., ... , /11'\' aJnaH'nj~C(\ sll LJna~6'19ne56 J'?>nC'(n0l mnmm o:JhcJncn 6JSnLanJ"J~' ?J~j3J(J) , % 5:1 c3ths I 'd~~j2f1we 1 ~ ~', ""-:;2., '~n' .sa U~Od:J6'd'(7JS LJnohc'J~6n n)'nL \6.1.I~ILJ21,"·, Il:-.nl, brncm f)... l1JmL JJ LnohJJ~bL t:Jrnhnl "JC'fHJ~ un. JC!'?J6'nreGrn ()') ~ A:::: f Cf!) 16.1 \ + t (~2.)l6:4 \+····r fC\hllh n\ :=- ~ f (\" K J\ .61<l . K=1 SA-I., J5rneJ~j [Q.,,%J L.JtJdJ6L9<bJ tc:n Llj'J61ltrH1L~naJ6[H f16tP1ohJC':lhfl '0J:ln. 0l'J .rhL:l~Il1H ol..jl:1n 1 hOO'bon, hm4cnL!>~6,Jlf 2nnL1lhJ~6' .fex) "1".lGNnnL hn8s<ln,. !iJfJ£n, hflleJwlI' [(1.,';] L~21<J:J6'[SJoL e'56J6'~nL '3:)!:Jac>e JnL"'J~~cn [,')o;):J6'LPJ'6nL ,lJnchJ'J,Jan ".lwU,0arle J[fIls,f'J:io.r6', SJ~flIJ'6'l hm') ~CX) ~':l6:htn.l n~JoM&r~nj [Cl,-tJ IJ132~6l11Jj. h,..dvOI1L tJ2~oL Sd r £tC"~Jld-, ~ll"'l"n~~ ~ .1_ Jm tYJJ":1( l~Q2J5lf'b~ r-C x.) ~"J6:tltnn[, 2>.r6lJ.fbC'3h!JCA n5tfJ o luUl eJ n'on 5e:nGn'ilbJoj und6mCr0fl) i) JB tCX)cb::. Sll",,'2>6e. B n C0 ' f j +(~Jdx.= lim S'A -= lim. L f'(~K)l6Kl . ~ A~O hl~ '.A\\\-+O l(c.1. ~ ~ K~n ~~IB6",j. :lu 'b(!l)shn sh 'j6"eS l'l'jmL eSdm~f\e1~~(f\ shU' [Ci1-tlJ LJn:lKL9nL es6'.JO'()t.1~n[; hJL<b~ es ,Shli ~JDj6'n(~~nl l'J"JeJMe d(l<!'j6!jcr'\ v~~3~c9J~neJ6' b~hc9nC?lIlL JhM3J<'b~. aj~tf1J.roaj. U'rr\Gl~J lim S?-.-=.I bn'l1tS% '6~aenL~ 6'j~nLJn.Jhl\ £::;0 hnu'b'3nLJm?JnL. shU~IY\,L oUt7l" d70 hnlI'b3o '1 h;2° [Q,-BJ [.,.n.J.1<JlJ'r10 L {, ~~, <rf 1::, n Ln2;J<J6':JdJe ClbOl-dnJhn l\L,jc:>1n eJ6'J6't\CJ~()L I Ol:.lnl, hfT\knL~?lnlJJu' ~LS ~.f s3 ~"}Uj~U'~~lleSG 6:J~n~d(\jhJe skf-J~(n ""S~,""'l~'''',"\n O'Jhtf'(l CJ6nloy>m Lh~ceJ~J "JlFrl)('fI)oJ IS'A-I1 <. £. DStSuJ~C"~h':lcn n~lP'JohJCnL oJf'1~:JLf'/'Wlcn ":Jn6.rJhLn. ~:l-~ ,)(h, t (Xi Jhrn. l~ tJ l.JJ'M.JEJ t5l(b:l ~bJ3:)t9n.,ShJJJhjm'::lilO)(\ 13':l6'J(j'OJ. 80wo ohJ~n~n(7) LIj~hm ~~I[)'.re 1 ohs~njT1l71, 0':£ cnJMn~, :i:=o.... es X =~ 3:Jl-1[f1)3JC'jhn Ii'h~J~n(1\J raJ2rn LJ~C')h':Jcn 3h':Je5f1h"jcfl tJ'fw-fJlInnlJ "3shOJm~n SC'36ndbmm S-nOl. DS(i~nbncrf)CTI -t(X) ~'Jojlt'f\n hf\dJ60L. "0Sdn S'A. L1'bsf.rJJ, hm3 J~ ~Jdn~ ::Jm~Jcn ~ <;jJW~J~n Jl'r1oj\yJ;n 6sbA'bJ 6J3rnLJJb'J,cn 1 d:JGJbJdnlJn 2shQi~"jcnb:Je(1L oasll(1)m~~ eS,dJ'OJ ~seSd:J 0l3f'rOlm() S'). am?J~\/.1JLJ 6.5bib<tJ J es'alf'hnb':lCn Cl)(\o'Jh Ol ~shOlm~L. 2SUJo'J~I1J, hrn d :H. C?3Jho1rnSn MQl...O:3J o:JS~crl () d6:l;V a hfj!' b n~Mn [fh.u'JlJ'f11lL ~shl7lrn.~f)LJOjG, 6sohJa hsLY "j~hf'l1 3lJ'nhJ LJ212.JG~j~5e eJ3J6stl'nn~01 [2.,-B] 1):JoJ:;G6'~, n uJ()Lb3J3J~s dflO1 ''j'%m 3!J'nl\J rd6J~J. bb?JsbJnhJe hmJ 3ol;tjJ01, lim SA =-S. ds'dn6', 2lsalJtJC"?il-vJCo nGO'JonJCnL 2l_}6'JshtPj~flG UJq,'jJ3,lclJ'J C'.f?>lJ.Jh01 "-10 B. ~ f eXl d1'.:: S. (l, J.~h fllISe, ().«)lJft ~h~cn (\6't9:JOh.5( f) ':J 15:r3JIJln, shJ':Jsh:Jfn ~o OJ r1 OJ':J6':h!f\fl eJ G ~ (J hOL sa l3 "J()}l!Ofl(, 0l1S~r,o)l)O) <>;f:Jamw~C'3hljCf) (lh"Jee'rW1Cll 19hs13L1'rlot., O-~,rhD) m 6L. -+-_-U..~..:.l-....l>-\--,-,---".....:....c.-'- __ ~-"-'~J- __ 2{ n6d'J~h:l~5embnL .f.jlJ'nCl~~c ~nhn'JJ[, IIJn3J ~1~(j'3() O1'Jmh')~~. U)~ ~""6';IU'ru (\6d':)oh3~seI"\S tlIn:!J 1J~1J2j6'~j, at:ln6 ()on ~2(\1!J.fb~;h!lGlJ Jd u13aj6~ ~s.a cP~{l[,rj~J. e~C»~J01 l.Js5n6JJ(!lde~om :- ~q}j?>JCI, J}.tIl&O\~ L (\l..1cnn ~~ 9.Y.Jo.:ftiOJ, b3:1cnu' Mllh3 h;J ~J- el'kS" hsn2:J [(l.~J \;1e4:l6&1J~h 2.r3flJd .:sh ShnL 'd~m\JJ~C'r~h~cl\ .Jd Lm.3~6L?b.J I ~c9roMMem~nL as2m 6':ltn!Af\::lhl\ t:;>O hnl1Q(\l-.)~~nL "hl..J:i\'ll~L (1W01n &70 hnll'~n, h(l'\d ~(l\ti J ').. ~. ~ ) a Ji(Jn6' I 5?- I \ <: ~ (we)Ll' I 8m LJ'J;)Xt) S'JG:Ju'n,i, 0 J6/)Jtbcn3hJ:Jcn (\6J1~,6hJcnJ, 5 9. in 3nLn k{\~w tJ2nJ, S:b&b) Olt 311wf-';l.j~(j~o, la~.g\ ~ 1a.ltl~J 'J~o"'&1(;} ~~:Jj(J:l.3J I ! S? I::: \S'A- I of I \ ~ \ )';\-1 11'1 I l < £ + I . (i) 3m:!2>..l0l ') .b.L l:::.~, . , 11", J>.."J Cal!] LJj2>d:J6'L9f)~ N6Jb(1(:J<5om In('13~'Jcn Arn.JxnJJ (lU()',n lf2J16LPJS{\ .., ~M~bCalJo.3f)L.t0' ?.zS. 3nS'J<1£'.J6' ~(x) shJs dJdrnLJflJC",bcl) [O\~J-ih:h .sdnlf/lld nan Sh 1\J6J~J '~h20'\LjCbC'~~(n .r~ Ln~'J6t9.if'le.rG ~hOl-~~(1\<bj gJrlw" ash-:S~'.l~Cm~lJJ01anL ~n'3'.lCnLbjJrnOl, 3.)dJ(J)(T)Je, hm3 .suJmnJ lli.. eJb..lh-R:Jbf1 J62,···,.6.n u'J3JJ5t1'JdneJ5 J3nhRnmm Lu:nJbJ~m ~2)'~)~n ~;)r-t5hcJa() 6'~()J.,dn'JhJ~ /M eS3JO::!O:!LnhtnU) l\L.n~· (b2m~LJb(!\ilhXm~nL ~J6m I tLX)\ hUdn~ ene' :MnJ- 3():)cmS~~L. d(1()C'J~L .LA..- C1J~, sdnL9rn(), ().rhLj~~at- 052 L-nll')6LNln "Ljo,f) '( i t)ji-LPncrll h01dcl\LA3nLJLY 1 H'>i)\ J £+ \11 ;- I1'N'I~:J("'+ I fe',llllnij . (Jfdl',6., 1M 3f1Lsh~'1Sd~(/\ \a-t~\//I(l\-le\ dl9mcmSnOl 1 ajJ~J~J \3'A\ ::: \ t(~\JlL1i\t~(~~)\lu\-t··· + tl~n )\bn\ \ // \ fCS"tll6{\ \- \~(~:l.J l.1z\+···+ ~(-rn)L6nl \ > <2. t I II ) hstY JM{lJJ(!'.~~'J6:l~ Li) .QlP(ncm~JL. ~.n· ~?l16'(\ eJllr.>:J~ dlfeJhrul, GlJfYlh:klJ esd19:1f\\Y:!~cnJ. 'd:l6n'(J~b J '2:1 acn1J.JlbC!'~M c.m~.shnL ooLl'1Oh1 ~J tlll6ltl ~1Y(\C')~'J(n "l lQ,h-J ~ .rns uJ-5dvhnLn .!\lk~J. dS6SC!WI H', l11 "j 6" ::tLtrlJ ~ (X) ::{ 1." nmLf.f X, nJu'oll\6' Jc~hnJ , 01 hrntJ'J X. nhsLYn/l'ltJ('jhnJ tJb5eru 8J-2mLdb~3h':'JCJ1.}' c1J2Jh..12 Je.3f1Grl uJfJ3J6J6:JC.nj, hmJ n2>n Jhj.) nb8:J3hjj..ti) jhiJ Jhm [~}~ 1 lfJc:b&%J. dJhmCJJY, Olj hN1JfinL 5JJ2n (JlOO1mJ~c. 6'Jh~nc.LJ J3nh~:J?i'1 tuo'l1m6JCJnLJ, 2n3ne'.JM1) hm3 SA:= f.. f(~K) ILJk"I::: n n K=:i. ' = ~i~K.\=£-Q., ,bmcm t7Y.1 J3nn-RBll1 (\hJ[f()1lI6JcJh.J~}~Jdf)S 5A:::~O'\6K\::O .J:heJ6 ~Jd,nina II 'd::JVj.k'J~'JcnJ hn3J6nL ~~1\ ~h&1() (LJ n3J3J hnlJ'b1l'\U:l dnnLO'hJ ~O'\e.J6'. ()6tP'.J'2>0'J~se(Yl ~n L UJ~2Jhf\L j()hrn~3S~ 2l ~c.B::J6 'd Jde:J3n Ol~mh:JJJb n: en j f'!\ '" 'J a J. (}')'J ~~6.:t lJ"()J 2M6rnt9m6bh\\.l hJnd~ l;j38 06'[%:J 1 8JI(Jn6 ()l r~lfJaM~Je().\ J;j !J~ 33)(5 d'q,j. OIJmh'.l3.5 . (hlJ ~~a:h)'r\J 1Jll"~1JtPrlJ hJ04') umJ6~<bJ' 2s'dllb nL n6l9JOO::J~se.nJ .$1 lJ:J03J6'~i{)J. 3tn~?JjO) f(~) Qs g.c'X) JA()J~ ta,tJ Lnd'J6'tYlJ'J 06'LPJ6i1J~Jen ~~1Yn:0n K-6:JtnLa'lJ~f1 1 1 d':lecf\?ll1, bmcm C - a.. as.g if:J~t.?n('J5L ':lrnhllL dl?16Ji1J 6::l.SnL.1~ b~h£2n(n. <ls'd\lb': () n-H~J+glX.J)dx.-= ~+C~)dT-+- ~g (~)clx 2) f K t 0:) a:r =- K J +CxJckr 0.- ~ i £ Q. ~ Q. £ ~J 01"j -Hx! ~ £ ex) , ~Vd ~6 ~+('X)~g ((ud'l: 't) \) t(XJdfC \ ~ J\ ~CX) \ d x £ (L Q.c. B 0.. a )+ C:tJeb: ::: ~ ~('.tld~ -+- ~ ?cxxJc.r . (}.. Q.. G. ejal£'~f)dJSj. f) Oljnlj~ ~cnJjJ{(he ;:'JJm()&)n6'J(,::lm,h ~.rt)/...J{,~)~ne£· Lu:l~L>AnLnJ tYrn(rn~(ln nn ~ L(-tCrsK)t~C~I'J)l.1K\ ::: T l \<) ~ (. )\~Kl )(=1 K-=- , ., .' 22. t>.r ,j nC:JOl <b(!,~Sh<bj, hrnl1J 'A. tna,)( IAI<I --)0. 2) es 5) Jc9='nlYe'~nJ6 "EiJCMooOluf. f~~~ . 4) 'l tnCtMot. eS1Js~~ntr.l&:Jf l.IJ~.shru.OJ '4j36"n~9}' h",~ -If (x) \ ~ .y.{~) ~ ! ~~) I eJ DJ(3\'f)~~ 0) 3) ~J 2) Dl?lnlj~~~n. d03n(!\~~0'\ .. nma, :. !l·f.CX) Idx ~ ~:~(x)(b: ~ ~\ ;lXl6ir. .r:bes6" .in ar3f1\aen".sMcML esWa~nO'~~j(n ~!f",cm~J 5) ~~nU!l.) 1 hma~clJJtf lIJ6'ujCb~!>n!JCl\ f\~~hSC"~ J ~ n rj n~h m~flL t1I?JnL~W' j1111.> , 8J'uPn3J~ :l£5>:y.ll"e~,) ~1):J~~~n., jbJ':7~m'oOio ~(X) ~~mnnL~nl n6'~lwcnl. a:Jm3:J!1hfl1C1l 'CM'Jsll!.nL asa~36'1~flQI~ 'j 'j::¥~ ~B c g ~ $ Ss: f (XJJx:::. S:: Si+S!2.:: 1 ¥(~)dx + ~ ~('X):1T. ~~---..- ........... ~ X (l, c o 0... c. B l,,~.rcm a6nca~6'~crnMlJ O1Jrtlh')dJ " m~rnh~a.L ~CTl~~Ja" .vC'x) ej "g t~) n6'O'~Oh'l~"enn Shn.Jc [a l~) L~ad~6'~:} ~s ~trJw. &'dl\b nJhi..2ili of (ex,)-nL ~ao'nh,)L e.s "Jene:lL J~3~d'I\iJ~L ~mhrL atn""~fl dJlM ?. ~l1'b3n lhlllJ r: -t(~)·g~)dx :::. 'A I:~}(~d~ (i) eSSlt910lrJllJ. ~CPl~~ 1 m t.J .M shnJG', ~:JWd.5an1JJe I +~J-oL ~alJ"nh~Ul ~s ~eoe~Ln a6'l\~~~~t1\ [a \ &J -Cb3. dS~f\6', lY\ ~ ~ (X) ~ J..t ~ane'm8, ~ C~) ~o lnhm~nl.. ~;ScnL- O(\6J~f\O\, ~;JfG2&.s, hm2 tn· SCx") ~ ~LX)' ~ LI}:} ~ J<,. gcr;. n3J6' ~{) dn~t\cn~&n "' ~ il (~)d x. 6 ~ ~rn ~H:x.) d x: ~ J.l l~ ~ &)d:c . (2) ~JIJSJ("'j~j('().) mh" ~~d",b3BJ: :U nmtJ'J ~~] ('Y)d x. = 0 . S4 ehmL (I) 'JL9rnCTl\i~- ~ne.ro an~e:'~~Q)" hma j~ .fb:,.) ~Hx)dx:o tS a",r:J"s 1 LYbJenJ 1 [~J c.Pmcm~J ~LhJjcej$J 6:1 ~(\Ldmh(\ ~ hI'ILTb?lfllOl~f\L. 2) hll\lfJ ~ ~0:)d'X:. '>0· sJ ehmL (2.) IJtYrn(1n~eJ6' a~J~6J r:n ~ )~ -¥ (:t) ~ (e:t) cl'l: JJv (~) . ~~ ~ Lx)dr ~ es ())~ Jl"36"Od6J;C1\ ~ . \:(:t)'l[~d:J: _?- ('1-) S: ~CTId~ J (Lj) s6' dn~fI(!\~~<n (~l-L brncm C'~)-~J6' :Xl ndJL 1 hmd h'\ ~ 'A ~ Jl.... h.~· 2,. "I ~:Je~cn. allj ~(X) 'J'~31L9nJ, o(llcm 9 ('X) l\~tPjoI\J~en [a.,~] -~1 eJ g(x))J 0 1 aJ~6 a. QJ B-!. ~Il'\ ... nl. nsHj~J~l, nl~O\n C l)j"t9ncn 1 hm~ I~ t(x)gtt)dx= ~(c) }~gLX)dX. 2,rhOlCJ'" 1 .fdnL. eS1JJ3£f:HllJ'.1~CJe UJ1.9JhOUlJ 'dJ~6n'"cl6"mOl) hrna '.Hr~3JtJn ~t:l6'flYnJ ~J~1CIll~L (1).0nL. ~alfnf,J(, @J ~el\e,l" a<m'a~an~jl. 'drtlnrH, CJrMlJ3t:J~'JC j3XJ J6'n~?I6'Jdl'l~JL., s:lrl!.Pm8 h!ll~Jcn- Q1Jtt C S'3nlPn~n ~nftL'~~L 'A d6"n'd?l~C(l\bJlJJ[J, j·n· 'A::: f. (C). !j'J~J210. 011 tb:) ~o~?f.ll9l1J [a1 f>1-Cb1 , ~JlJrl6 {1 eJ fJ-Lt 'dmhnL ()JhLJ~3k nU01n C 1 ilmJ l~ fC3:)d'.X.= teO e.g-Q), ~ I 3.sM>olJ' ~ JanIJ es1JJJl!'1fllY.J~CJ e 6n6J 'd'Jen'd n UJ1dJhnLnJ S3oC"mO) Q LX)::l i es ~J361lJ- 6'0\01., hmd &"6lJJ%C!'3h~(n n~eJ2JhJ(j)L ~.roaJht9jane..l'6 2>J~mJen6".lhJ rf>i.ax= lim t. i'\~K\ -= £-a.. a. ~~O K:1 ~:I6{\~MlJ· o.r6'WCbc'?lh~cn il6'LS'30hJCf' aS6n~hL9J~J l1a ~JdO'l~.BJdntl., nIM'JU<ltY [\ ij £ . Jd ~J"6Oshl9j~n~ OlJGJbdJE!: hll\O'J a-::£:' a.t(ln6 I%-t('):)d1.:~O, brnc:m hmlfJ a:;,£ JJ'Cn6' 7 I: -V (X) d ~ ::; - )~.f (OX) d ~ . ()., 23 .Ie OC1\ 'a~1JJdm~a.3~:lCnJ hll\d aJ'tS1JJ'b(h~h~Cn 05'c9.3ohJC!11., 1) ,2,), 6) ~~nL~~j~n ~J 1 UJ'a~cm 36(\ ?l6~m~O\, 0l~h1aJ l>J"2J~cnJ6n .rnn.z6' 6j~n~~flJhn a. ~J -£, LJAe-., hj!nt ~~tt'lb3J3-J~n) .fcJ,sL8'l ... ., ) 0l30L1 J ~fJCJ~n h j~" a.) £ eJ C. ojhlfn(~~nl ~OLdnJhn dJ6tJ..3~nLCl6nL. OJLJI "aJJb3SJ ?) .s Lt) OJ ;nL~~6~, nLn6'o 2ls£IHUn.s6 a.rh:)';3~C lf3("nn~3~l-· 1J.ro3 ceO\~ h, hJl\ IJ'J a >£) 3) ~.f~tn\ ''In :!!9mCIl\!nL 6'rI~E>n 0t13Cj~ \)Jjn"nLj"h/II~lh hra em;': 4) ·_OJ.~~f\ l/~ 1d :: <~()' 6j~L3o~hl) u.A>~'h~OlOl~Ol, 'I ~3Jeme, £n '16'e,) ~J()t}'j""'L \ }:t(xJcb:\ ~ \ ~~ I t(~)l dx \. ?:>~:!3JO'I 1 t(x) JhnL [{ll~l ~1o:lj6'lfli>~ 4t)IPJDhj~Jen 1r3l.j6'~u'nJ (:5 Xt'-[C'l£l St:!'?>6,,:J6'ml7l F (X) -=r ~rx.f (t.1Cat ~ a. n~(Tl6..11'Ne aJ61JJ~~(' !=UX) ~~6':t[]'IlJL ~ilme~~J tLx) ~,dtfnnL n6"~:lahJC1'l l13('Jf'n~?eJ lJ}b~3hl\ll. cnjl'l)h'JdJ. (71~ ~(X.) :J~~~j(9nJl 2Jdn6 F(x) h.1hJrnJ1reilJ es Fl[xJ"Z ~(XL es2L9-:)nLY:JSJ. n6£9J'3hJcOlJ sentfn~hl'1'l~l ~~LJ~n[;J eJ !J!8~JCtn (f6'~onJr.L O)jl71t...J2t1L 231hh~ 'a2e1~lll LA':Id~CbJ ~~a3I\dcnJ "J2J8'~hl!l~ t X + DX ~~x :x:. IX {X1'~x. {~ 'fCx.+1Y;Xj--£"ax:)=~ ~(i:)dt:-r\ti)dt::) -+-} - J -=} f(i)dt~ +(C)'A , £t {i a..;):. Q.. X. UsQ.sti C. ShnL r:t. eJ c;r+~X -IJ 'amhflL a~J?iL1~~Cn llJhLPncn. J':lj&6 fL~+~X)- f(x) ==- -tCc:) . .6 x- QY.J .rc3 otn(O\~J~l\ l~.rC6'l q,("~1, hf'!'llYJ l""iX..~D. OJ'M~COLb/'l6"~Ocn ., h"a J3 ttJ/'Il~ c -7 OC ~J ~ '?>JO'~~I\L ~.ram lim ~ Cc) -::. ¥-C"J:) 1 dn?ll\(!\:l~m esLJcJ~(f~~ L9mcl!'l!JL. c..... ~ I'lL~e;14..!l. 6~n~n::lh ':l8'~~:Jcg '1"j6:tlYnJ!J ~J-RSnJ .:tnIl3x:lm'Sl\Cn N <1f\lfl :J1\Ql-'J~fl'In ~nh,:)rJfl'I ~ncns ~I'\ t.tI oj n6"L!3~hJ'cl) thcJ~n <b '.l~.5 1.Js<b(,\~h nolo .:lL O?l~~~CJ .r2SSh~~l, ~J?l~1\L OS\'llJit~"3~~c es ~ldb('l3hJC n6'LhOh/cU )mhnL eJ' .r;]e~Je} as~lJA(!I~I\"'Jc 06'191oh..IClJJ es 1l.Th3Il1:W:Jcl. ~llIhnL) Jdn£9n'2 8JL Q,matJh (\<S'LJ'JohJClJhn !!.I en<!~hJ() !fuJetlhn s(!'hnO'b?inl lnl\nOt./l! ~ha-:lCJ!JJ It "J li'm~:l~~fi' bole 2 J. Ul':lmh:l~U. 6'I'J ¥tX:) ~~~,:llJnJ [Q,~1-~3., P('):) ;f1 anln 6'1bnL;l11~hn 3nh~1("~/I1~n((\.),af'3n~ J % of c"X.Jdx. -:: '1? (£»- ~ (Q.l . ~ IX esJ(5'~LYj&>. 2lS6'3nb"c:lY\~ '\?('Xl-nL Mcr'nhJco tJ'?>(Jen <b:leJ lJJ<tC'3hn~ FCX);:) t(tJdi rA hCl\omhlJ' -onlJ'r.Ol, l=(OY) Jt\nL tCX.)-nL jhOl-~h~n jnh?10C':im43ncn sdnrfm:l PC'X)-=: j=('Xl-t- C. a;~n6c 1 1'(tsJ-CP(Q)~(F(~)+C)-(F(Q)tC)::= H~)-F(m~ )~H-I:JcA-t- )~ft)(H:= )~t(-t)d.t -:: ,g-}(X)d'X a. (J. (l a.. '4:l6o(~r¥lJ. Gl-:l S~?l6'f):J£J30') t.:P (-t) - P LQ) -::. peXi \ g, 6"nIJdlm _ CJoMi'nLlnl ~OIha':l~J :lM\(!' j~L lIJb3 J.. % '6 0 . ~ +C:K.1dT -= PC'):) 10. . (1)''''hj2S. ~m~~, .f(~) JhnL [a,B1 !'~2laJ6'~j ~m:Hfu ~6'":fLnlJl bOl(1'l) X::-P[t) jf) - ~\~J L:rOd'6~~ 6s6lJJ~?1h~CO (l~~i' c.:1~3:JI.9U ~am~~en OM6":hrOJ 1 h,,2cnL a~~an&OlJ Lnd~JaC::hS [a\-&] 1 sJJ~ 'f(cl)=fi. t'S -f(~)=£. a.tdn6 USdJNncnJ6hJ ~rr.M>JCJ )¥'t(X)d~ -= (t(f({))-.pICt)di. 2'-1 Q.., d.. (7J:JmhJJJ· U)lj 'U CX) eJ vex..) ShflJ6 CQI-Bl LJCdJ6!%J fjoBJcHe 6'Jh~~Jen G~'J6':Jlfn:»o,aJ(lnG ~£> I ~ (t ) 11..(xN LX) dx = (u~JV(iJ) - ) UI[Xl VLxJt:b: . ~ ~ . 03[; O1J{hh:J~jbn dc9-:>f\(ie~~lU6 ()LJO'\n?~ tl!hnO'l, h()'\2.mhl\lhJcY 'aJW~Jd(lL.n OlJmf,:Ja~n ()J()~ldb0?h~(n l1o&ni\JCnWD!?lr\L, cr.c~\(i\Ge LlJChSbJe.m scof\c.lL ~6U 2Ddfl1Mfo1~6rnc1\ 6'n'J[Sl(h6'- c.JMbn!lnL "3rnha~{J· LbJ§DQI\t71f\ 1\Jbr\L. 'i,h~xn 02,n2,~nru.. ~shOl<MnL ZL\2frolK~ z&W~Q' ?Jwn n&t9Hh.s-c(\L LJ.s~c..:1sc~:iJ n D"t a~O\cj'li, h(Y\(2~lU(]' n. ~"jNtrOJ~n shJ~j).jm '3nOl6'o JhMQ, ,,6\pnhJcnL 3j0\2.:lL9hnt)cn ~f\6'Jshhn~ Q.(.lm4en6Jh:J, t;lja?lnJcnJ CJ3fi'~"m(1) Cob- I) S:::5:r.-S.: )t.ttxh:- \B-tIC:C~i2:·=-\~[-t2C:[) ,-+\0:)] d x, . (l &.. Q., hmQ:lu,fli :lL 03"j6':lU'nJ~n .n.. OI\f\J~ .ThJ~,.MrY' ~f\mb(), enl;\3JLPmO\ aJO\ nWil1(\ C. d-':JeJn':l;f) 1 hmJ I a[)Q'J~JjC(\ ~'15·:hrI'lJan £ I eX.)::' -t?~ (x) + C- eJ SJ 2.['.):) c= tz.[xJt c, ()~'3o:l6 Sf1J~Sh:lM~n!JI6'n CJUOln C 3':lean~1\ ()shU~:l~L fiC~:c)-()L 1d.13rnLJt{,Q\'!llvjCIl\JnL CJdm, lJ..rb'Jc::(?mSh, c.-I.- n0\cdn '}-J2dnJcns3n (:\ll\D\ +ILx'J-I1L lja!.Y(\f,Jlr'l 2{i'r)';h6K[l')6J,fi JSLCbj 221Sn 6'J6nL2n:J~(\ 1\l\Ll'b?Jo'J. lJ'w-<?rlJ,l-.md ~LC'X-) es ~L(::X:) -·()L 2lhJ31\~1bL 'drnhnL 2m;l[11':1(\\ q,no'<Jhl\L ~5l-..D1!'f16f1li !)jO~bJ S. a3J:TD.J~j S = l [ ~ 1. (~) - ~ ~ CJr-,~ d x.::. ~ [U~CXhC)-(j:t(:c.H·c)l ctr -::: kg [ -t~l'x.}-+\[X)J eke.. . . 21 ') ,tcX-) ub:J>jcnlJ amlY':lCO\~I'\L 6sJmC'\1C.\ 2Jssn3n 13'JOl'1DnL ?nbJ ~3n01· b h':w~n01[) Lb~IjCf'lL 3Inlf:'JCir\ ~ nLJ e J ~'JG3n(M Cb'Je.JJnhnL ~Sl\O\m~nL ~ m hflC"J ~n_ ~0'l-j'3jffl, OY...Y~ 1,Ir3l\tYj~n C1mlljd!lC(\J hfn4~ 1.Jbj~Cn, hmacr\l... QJ3Jncn ox C':lhd9!j shnL [a., t 1 LJ32>a:l68'n. ~iln~n:lk 'X E: [O.\~ J b~hlif\~~ Ds3S?l CfT\01 o':/.. Mhdr.L 8S/V7 ' ,r, ~1Ci1 lJo~hl!j~. s2 Ul'\~@~f\LJ e.s 1JO~~C()L ~.r6S1~~(T)Ml 3n/!lJd~cn ~no~hn~ 0?>5hO\mM 5c:'36'r\~6l1l()) SCXJ-fW).. hmli'S X. "1J'3c.:j~5 [a \~] lJ~oJ:l.6't9~, c;Cx') 2rn3oO"J3[; ef2 L!.J;32J6&tJj Cis6LJ}6C"::lr,()C ~16'::tU'(uL· 30d-':! I c.[)Lba~ ., hm2 :lL 03'jC5!ldnJ c:Jo~~~i9nJ, 3Sd<\G' am(y'JJ~Kn LJllj':lCI'\L ,8(1\if:Jcrr.tJ 2sdmflOt3('Jd J ~rn/lJ~{Tllh V = 1: sC~Jdx. . (1) S.d 'ilmrS~Cf\lJ eSLJSdlP:)r'l(J'j~cse OIlD5LJeJ'Sil ~1?>6'n'icmO'), hl'r\d 2,,':) eonh:lcn dJ"hO'\(\ cIilCTI6ehnL Jmd'!J e'lJ\f, J <mLn o,~.Jl\L o;;s},o,l'lI~OW e.5 uoMa-cnl bS'3hJ3Q\L !SU\C(lJ C s JnL. u.rJ(3~6':lks e W<l(l..rhIllJ1 J oSlf3flOn CffiO'\ l\t:.X)\() ::lfl'O'(\ ih.n<ta:l~nL. :in2e:l~hrn~J., hma~CCAS lJnJJC'C~Q(\. rYnc()£'eh",L IJn:lJC'\:::l\L LPtllcGO shnJ6" ~J nmClKO\J ~L ~ 5h"N\$~~() <tJC'?lsl\"dn 2J3sJ(r~.%· u'ncn6'ehrYu 63~L.. OjSM)(I'~L) 25 I Od bnhnt. [,nahd~ 1 bsh:lm~~J&n -¥(:l:l C73~6'flfmL ~ Sd ~l11h~~ oL ;. ':1 .. z:. t'.r3~m", falt1 Ln~jt5£9n a-:xo L L x~ L···.,( XIC-~ ~~r<:<:: X"-I.tXI\-::::.g ~ C~~fl(]) ..1~~A!2.,··.,.AI<,··,~n w;:x1)6t9.1 ;' , $st'. sd !Jj2>d:J6tP:Jdoe.r6 ..r~C' m <n bjhiPdn 1; h ~2..,. 'lC$'t< l"'l~n liJ (nnJlOl~"C ~ I( I ~ I I I . (K::iI2"")h) bj~r9r0hj as3J.3anCl OX Q\1hdnL I 'Ji ~2' ~K ~ ~n-~ ~t\ X o a Sh01~{lQ) uo&-.d'J:J. 2JoS5"3nbn OM1 j3~mJ'dn In- y Q-::X o Xi···X"_i XIC··::fh-- i Xn=~ ~J~{1cn '302i.Jf-J P'Mj,NY'~n" ::>()K)r;snL 3j,a"-bOh:Jcn t.lt\cr.6ehn ~ hmdCnL 02>~J~1\ sa ~ni3'JhnL LPmCQn ~rv6' es oJ~rn~~S6 x=- XK-·l (ls- X =Xt< LJnbN.9~Jj~'im. hse3Jb s2 lJ'ncn~ehnL q;a.:!nL ~sJ.lllO\~J S(~K) 1 LOdJ('\(j -:In 1.,61<'11.sJ,lPrrJ Jnlil Jrn[fj~J n. n jEJi2J.) S (\;.K) I.&K I. 0d lJ'ncn5eh:ionL ('jJJh<J1()J6fu amO:Jl1':JdU lJbJ~C!.J, hm3cntJ 3mu':lcmc.) n.:HiJdJ ~1 SC~K J [.61\ I. non ') ~C15eme ... 6J.6Lb~3~SJj(n o-:!€~6J dO'lY:I3xf\ UJ311CllL 8rntr.ldl18nLJlJ6, dsohJa l>'MeOJ, hmJ oJV' a~nrn 3s&Ji\J lJ:laa1W~ e (lmb1&s eJ~m~.) , an&! ~ll3hm :fltflilj .,~~.r .i L o.ro1AJ3J3jbJ. !I- n· V=Jim ~ SC'IKJIAKI (~:::rnQ.x 1L\K"I) , rI~ 0 fu I ~ K ~ h. ll.meS~J li, 01~ asaf'lblj6~b01 oS6'uA03~XO 1\6'15'jahJcnL aJ6'4Jr.LPJd..rL, dll3n 0J~m esLJJt2-j n (fj,j:Jc Ojrn hd ~CJ L. 'U1J3f)mo Loj'.101L a-1l'I()'~(ll'lJ. n~ LJb::l~C()LJ Llmlfj'jeml,.), hmd~01U' a~Q'j6.) [Q,gl LJna:JDt%.J jhJ'J5h.'im~nmn, :Jbj~Ji9f1 -Fcr') ~OJs-:hml\L ohJ'~()1r\a1j es X::: Q.., X:::£ ?J:JM£\1X1hn li'1\q,~~~[\(/j ~dmlJJb(l13i\~J(1) 3h-!JeS'nh.I:J ft'(', i O'hJ.rjc'f1oIlL ~~6"3()01 OX C':lkJnL 3Jht;bJm) <;s;)mMI~C~~J 0301h2'l(O!7l V == jl I t'>f2 CX )dx . (2) (l, x s2 ~<M2·!1CI\L e.rlJJ~(j~nLrj~CJt' !JS-1dshnLnJ ld336l1~iJ-fY\01 x- <:fJJ tJs2J~ cn -!J~:Ja1J Ji-nL ti'h11 hmJcnL hJ !,1~l,nJ "r -=- fcx) e.J :J n. S (X;-=- 'Jl.1z.. 2.. :::; .fC -?:<'cxf . a..sldn6' en '!fl\~CneJ') dn3~S~ C2J-L. dCY~r.Lle:J~)) I1md O\~ 1 ~..fh~J .5(]NJJ I ~Cx) ~J-f&JU)J JjQ'j3,jcRJe cs1l'd:ldrn 2f\Ln ~hJq,[).,()lJ 6h".lG"3f'1O\ dnC"lbJ.Jcn Cb3e.)~i1hnb ~m~n.J 5= 27r l~ -tCX') J1 + [tlCxll~d'x . hrnJ~(()I.J' 2mntlJaJ [12, B1 L~M16'tP'hj ~~~~J~ ~Mn(J1, Ma~OOl~dbJ ~h3'JCnOl = ~: )1+ [t1(J:)f ld~ . o eSlJIdcl'jl\(JjkJ e l?J3s6"Jb\)Cm01 UtI BJ L~6d~()C§f1 O:;:~<:.T 4": ... <:~-( <Toe <... ~:x,,-\ < x~~B tljiililn[~~, OJJ16':fu1I\L 6h..~M~~ s~nC'm(h I(hlJJS-J~l\lJ\ J,{. ~ .Ru:.... JLK-4 ~ lLr::~ ·ooL J1JH<::: lln b.1hunrJ6n, (r1~ b.lh~()(L 'ilrnhnL :~5iXll\Cl\L ~\l\hdIJCnG esbashJ~f\B\ 3.rdm?l01?l.!C:(l\m s:J bJht9nobnL %3sjNnjb3Cn L5'jbncnL U\cildj f?- (jl:::. = mCL';<. \AK\:::''rr\(U< (XK-~-{)) 1 \;~se.m SC'ol\C.sL 2JSdm?!f)~~6mo-, l!"sehJ6{]oL OUmh:JdJ (!J 6Jt'J3n i6)(~h i~K~l'\ t':?':)(h Q)C135hCD.'J ~ hmQ?:Jll.rO' ~~O. 2sh(hCJlJ' h ~::: ti h"\ ~ 'A :=. ! i m (I J,{OJLl 1+··· \ Jz.1<-ieU.1C \.;., .. T[~-l tU.111) =.1 i m L \ ..u..K-~JLd= I,\.... ofl " .... 0 ?-. ...... o K'=-I ~ l i ffi f:..j( :rx-Xl(-~)\ ( H ~/l--t? (x 1<:4 ))Z' ::; jim ~ .jr-C-:&,---:--".:r:'- -~_--cd~J+-:-( f-'-C ~-K-) (-X-j(-~-"-. TK---{ V--'<,J = 'l.~o K:.~ ').~() lC-=-j := 11111 t. j i + rrC)KllQ.1 CXK~lC-i) :::; l,'m L J1t [t(c~K)1~f lLiK\ ::. \~ M'~~(C~'dl:tl dx. /-..-4-0 K::.\ 't.-.;.o K.::.l a... 26 ShS1JS~"jmhn3n n6l9.J'2lhsCl~n Sl\J\;s61j61hn II 06'a>:l1NCiI 1j1JJ[)yjem ~':lrcJe'bj. ?in:f~SO'h ¥CX.) Shnl Ca..,-t c£J) ~-tl.rCle<bj 3J6l.Jfb~ 0~' en (lJ.j6i{\ 0'3~6::liinJ ,hll'2xnLY n&.P:l6h:l~sl2nJ ':1m'33c [a,t:1 c[(l,+<V) !Jsbnl Lr~'cJa~6~j thJj t ., Jhlj~mSL. \ imP: H-:r)dx" arlf\6 Sdd~JS1 krna ~C'XJ (\6'L9J6hJ~.ferlJ [Q..,;-oo) 'd~.rClf.C¢j shJLu~~Mnjn i-+ +cp -b, I"t- OO /Mr.(/) 'I Sd CbC'351\L ~6'me~aj6 5hJLJ~J101hn1 M'L9johJCl (}S dJL sLJ SC%'n'd6J'3%': .la.- t-(X\Qoc ..rliJ(ffI- oi\\:JnJt' 2JsGnlJJb0'~M$S n,J!JJ~Ij()')r.n<l(\ (\~.nllJ(i\ (-COlt] IJJbf'lL. i(j~JClecbj, bm<:m C-OO)-tco)f(/~J ~:l eib ~ .Thu"LJ1>;j(hr.\\1n I\t@~6hJ(T) 2u6nL1bC'3h~6J ll1m-arnNf tif\6'J mf-.n UJbnL fl6'rP~onS(DIJ f:iJd n. Jdh"aJ~, (-toO' 1:. t t t= ~c ,-\OCO j teXJdT-~ [im \ t(~JdX? ~ t(xXb:.~\irn \ t(~)dX ~tcx)dx=)ttr,)dx+J t-cX)d:x:. 'I CL -\:;-H~ (L -(p -\:;-+-co t -00 -0"' C. . (rr>~C(\ LJJ-R3~6:Jh~nj, ilffid ~~JGJL~6JCn 15sdfl C hnLYb30L J),-.g'J3J~:J shJJ <?JJm~nC'~~(n). (])~ sh..sGJ-!l!J01hfl~n f1{)LP~ChJ(n .rhL'J6(,i\~L., jd~m~j6'., hma non ~ h ~ 'iuC:: n.J ,bl\6JJ0d(!~3 ~j2£nbiJj3Jgn ;)[\- 2lS6'&J 2ru . to? d 2J~I;J\C('f'(7) aSaSCf\(1)o, 3si':~~6ft\m, hm:l \ :. ~~MlZnJ" hmLfJ eX >1. e.r 3.r6'd(J(Zf1J ., hrntiJ cJ.. ~ L 8shO'lCSU', hlllO's c(:f: i ) o3J:l6'J~j { '{ hm(jJ c\ '> i )"',00 dx ,.;: lim ~i: dx = I irn X--q'+l It -= i [i rn (4: -ch~ I L::. d=i) t XC' -t++ ro 1 r -t.+t(P -cJ....,. 1!i -d.-t:i 1:~too , + co ? hfT\()'J q <.. t ) bmc(11 , hml1'J a-:: i, Qlf\3f\C'J~aJ \+iX)k =- 11m \tdx == lim .enx.\l -:::: 11m en-\: =:: + r:/J. 1 'X. ~+"" i X. l""1'OJ t 1')1"00 Shsus-Y1(hM3f1 nGc.f':J3hsC1l "2J:Jrn':Jl\.fbcn.%J(n (ljlj6':1!J'nn~s6'. ~(/)-j3J(h, ~C2:.) shn~ L Q1 £) t~r~j{!<6j oLJ(/)(\ 'll:l3m";llJ.!b(ll%:lCn OO~6':1ltnJI hrn3.Jcnlt (\6tPj2lh1~Je"J jm!>:lC' [(lIt] c.[alg) usbnL ltJ6~6(JJq,:l CJ~ ";J~da.bjD3JQln Jd6rn$:J6", hm~ -t[X"l ~~6'.t !fOuL s:l3L M6l>J~-:JO'1hJ~~ crnaJ .g, OjhJlr'1c'(Jf1). n 6'l:9JOhj~ remdoL J-:>U'n (J ~JC[) j()~ffi~nL dJrnm .fL:Jlnn 03":l6:hfns 3:lh I\~JgJ n6c.fJ3h.Juen ~rn~~c ~~JcJeq,~ , J03hJ2, dnIJMe53Jf SCrllJJ, (;Jj{1.J{~~J 3srJ6u' Ji[.j~mSe~L lim jt +C1:1d:::c. 01:J n Cb03S}.(1 sN.J~rnal , Sd~m2.16., hmd -R"T) i~ -Q.- a. ():!,')6:hYf\J n60'J"Dh:JbJ@nJ Ca, g) '~bJCje.ChJ Sh.rGJ1QO\hI1311 ~nC!l, S:J rtJ03Shl.- ':!bMe:J~JG c0uiJJ:H10in1\3 n6'iPJa hscu eS asu K~JJJC1~kn3n noLPJooJ(nL dL3s'3Lse scn6,<:lOJ?J:l6: \; +C'.:Cidcc .5&s-dn3f\{JhJ~ 2.f6T1UJ&n3t&J s1uus1'J<T\M3t1 n6"G'J3hscn C(L, BJ l.JstJnl 'd'1)L.}txM (\;) I(JJ~()1b3j3/:Jf1) r.rn~:JL5Lr' ~0=) ~~ojL"nJL 3J61~J ~''J{rr.b5 sj3L a. oJhl9nC211 ~ bmcl'!1 oj 'i1J~b3~3/(Jn hm~~u ..J1Y ~X) ~'-'j6::hJf\Jl OJ()IJJ;E)aJhJ£~cmdJ .r:f1JL 1 [0, ~J ldiJsc:lenL f\(1\dJCnCiJL! '2ncJ C 6"'jhtS'nc1dr, t}s'"8n6 ShJuJ1!jChhl\~n I1"JlJ?JhJCT1 S.a r:JJjJ(-j~j M6hLJb 1 Q 1 3hJ6J.,NnomhU [aIC) f!J (c1£J 'd~JC.'Ie9dtfu shJL.5~!J01r,II3f1 n6'L9j6hJC:J~nL 5J"3n .J"dMiLe, -RJdmOl3CnCn l(lJ2(f\b~n'lbnL 'd:lW6JdnWe: \8H~)dx-::: Ii!)! \ttCX)d~ J8~b:,)d~: \lm \£t(x)dx 12~(x)dcc.:::: )C.f0:.)d:;.. ~+ \l?to:cJdx. j 1 1. -t4.Jt,- a.. (l t-) G..+ !L Q. (, S:Jsli , m~ shJLJ-:l~()1hnjn n6£1Joh"cn Ji-.Lj~mH , 3JL ~6'fn(?j~J ~hJ~,reo, brncm 0'f.lSlW- o..(E~(Jen. 3sR'.l:lb~0I1hmd r'd~ ~h~iJt[)J 'lhmL1'J o.<i es 3J~(JC:(1J ,flmtiJ c\~:L dsh{j1oLl,' o X'""I I\01LY S d ~ 11 dJd o() r ax = \I1'n ~i.doc =- lim X--<i+i II.=. i o x ct i:~O+ t x:>- pO+ -c\+ {\-\:; -c\+ ~ bmCrn., ~mLfJ d. -::-. 1 ~ a3~}6:J~J ~!. d X =- II m r' cJ. X :::. l i n1 en X \ i := lim (- en -t ) =. + co . o 'X. -PO+ t X. 1:~-\' t -Po .. 2"?- 2Jf;t!'mcJJb. hmd:JCnJl' :iJJheJ 2: Jh.:J'!JdJ.5"tfhu wdnmcn Y=~r:r) fJ'Jtfjr(mw, d.JnL1'J36 J2/JJtn3J JJ ~&!l'()fJt bJ!J(JfT)J?-X.JdiJ n h()3JJ~'1 RJm301m JOff)c.:idJ IJ -::mn MJnt %3J':XJdhil3fJ Ol"3;l!rJliLfnJ dM &;;1f1nc:JdJ. Jb dfolfrn oJJ 2JYido<3J .jfJnDJllfrt. d.JJe:Jan lJJDfJ U1 F{X,y,y',···,-y(IIl) =0. (1) 'j-:::: H1:.) I7J::JMIfWu, hm.JcnL f1.JM.JU' (I) l!mar.,(3.kJfJ _ld ti'Jnond.JLJ fJdfJ]JrnaJe dH'JKfLl':J.36, JOrne.:kJ.J 1/) ei7"3.:J /J.J!jtln.x:::J!'J/I t3Jf).tftncJ3nL J.lKM5"JIJU6fJ. nLJ:JO? Y = f (:r. ~ C, I C 2>"', en) OJ~fjjunJlJ, !JmCb"n/J' , aJ!JeJ .r J!la:Y~ J./ ';.'J!JtlJ3LJ .Jb\Jl1lJ:J h Jr.JC eJdlTl'::1Jnt!.Jdx d::re.2fJ30 t!J },mcbc/){Y Jd ,]'j{!dn3:;BnL !i)Jnl,,?/lJM dJ'fJd.J6.]O:J<1.Jan!JJffJ3n L JJd.Drn'!3fJOab (1) dJot!Jno2Ju, JOJ7!e:JdJ Jd aJ(jJiJnc.J<3M gmMen .>drr£.JIJwl _ o:fJMfffJJLJ, hmoxfJLJ' C'f)fl(!'JdJ ~m Men JdmIJJhJ.£nuJ2Jo d:yedn3.JdnWt1J3fJb .:Jm6':J!IJtP.!:7CfJ hfllft'J3ntnl1 d£.rJ~3/J.:JCln<3:/anL dn&7:1rJ2/)(J) ~ .7S'rn e;aJ dmffJ ell efl'!3:J!l:JIJIJ115CJIvl oJ/)l!Jnc:JML :j.:i0m .J2m5.;bL£n . }fJ!J3.:JdI 1i/li'Ji7f., 1:3:J:J'c.kY'vl3 ej)~dhJC:Jh aJob'mCld.JL x/3fJ bJbJ: Ff.z,Y.Y')~O. (7J~ .J'.:fJeJ£ y'-b dJdn 3!J.JbJ30? X eJ Y-o[, b.J':1::tXJlJ/JI17, /Jal1 dNlt:':J?L fJ.Jb:Jb; Y'=£9(X'Y),Jb') dy .::: .{jtx,Y). 3I1J:!3J(J}.nw) dx LJ'3CsenL J (x., '9) C!3~E:J!Jh.J nl...Jl1¥lJ' hm2 nan DJA2/Medll/J:JQJ JJ'Jc:J:J'!JCn It'.3C5e:k3nt ~'YCjiJ"M2nL OJdhJ3criJ WOOt1J, J.(). ;J(x, YJ -= ~1 (x)·J2. (Y). JJJf!'J(J~01 dJ6!lfnoaJ JW 1?J3S.JIlmm: dy::: Jdx)·9~dy)d:r, L.fi/t!!J10lY 3{!}.J J~(100) , })llI:I fJdx)·:h (Y Jd:x. - dy = O. JiJ.:Jn {jJ!'dm5e;lJhL 'J.:kJ{'JM 3JIJ-,ltnodnL ~Jl>dm 6..;100 (I) .Jd OJEtPmc .:u:J-JD :JKme:iJ-J I£rnI1:Je. 3.Jbll'JC:llJ,<}tr3C5e.J2ru!in j/llJ3.JCf) hnarL f31f!9.:Y1J&rvc!YY1 dJ£tffnC.JdJ· 2nj, JdmwUtD oe .JJElfmc.:i3nlo rmfl3J 26JhJ aJJJm(/} R dX)· /12 (Y) &JA.;3/6J? dn3fJf!'J307 3:1. (x) dx+ R2 ('j) dY =. O. fit (X) J:z, (Y) J R2 ('J) dy :: _jJI (XI dx . 112 (')) f{1 (X) rlit.ffMJoOn6 5c:':Jont 'dJ2e:Ja J!l3fJe:.'.Jdm A (Y):= 13 (x) +C UJM1.J fPmarl3JL, !u(){!..sD.JI1") (J}:J 3.JdmJIJ.:lu3m Y-fJ, onJn{!}JJ(J) b6frAJel (f) .3JDlIfnOdnL r'DrnjjJ(, JJmD.JbML: yo=!rx,c). Jnl13.Jcn hndnL bn9fJ3n ~n'!JJ!lhmJc'!J/)n a.;EifflJoJ.J Q(X)/""£[X) Y+C{X)==O W6flL dJ[j,pmc:JaJL" bJt:JU' a {x) , gad ej ({:x) JmC'::kJ':Jol ~J;;.1(,J/l.jJI1J ,bmcm y:::: {('X) v.JdnJ2DOl '?J"jQjlt'f1JJ> .JDmeJa.J inIWcn hn2Jn1J o~ en'!J:JJv6'Hh.Jc':JM o.J6MnoJeJ· (}):J (lfx) '* 0, iJ.s&J1'mcfl3nL aLX)-'6J D.J3h-I1.n))Jt' 3.JJm'!3ntJl dJb a.l:il'k!OJJ dn3n'..xn Lu.6.J y'+P{X)'j+1[x)=o. (n Y I I I 3JdJomtTJ (1) a.JSJ:PmCJJflL .x3rn1J.J6!.£n Y =!lLx) V{xJ u..JDnOJ. hJ~c3J() =1..L{x)V[X) -t!.Jlx) V (x)) iJ3J.:IO.JCiJ? r'>m2 ( LL'(X) y{:r.J+ LLfX)v'(XJ) + P{X)L/.{;;.:J Vex) +- q.(xhc () . JnCCJIJ':Jc.n Ifmc.rr1OJ J.J~J3r;Jhm(JJ ':J.J2eJ2b.JflhJe V{X) (/L'{'JC)+P(X)wJeJ) + (LLiX)Y'tl:J+q{X)) = o. IIDJt:.I1J 1 C 2) fJ'mctrdJ dJu,:JceJOJ J aJ'j !lLx) e J V( xJ q:j :'JD.1U'n:JdL nLJ ';):L3.JJJ~.J3OJ, hind LL'(x) ... P{X)LL {X ):::0 (,3) (!>J U{X)V'{~)+ q (x) =. O. (I.; ) ()J'J 0) dJt5iJmc.i(Jaf.!..fD 3/drn3f}(f) /L(X) -b J 2.J.JrJf!JD(f) hJ d';D f L;) iPmctrdJC!n 3nJm3rJdJ V fT) - !.JJtI I (J1 ()J2JJDJeJd.J J 'Y-uJLi. f3J-oo !33J:/Ju J /.t1(X) J li (X) dx = - pcx)dx I L,JneJWfJ' en Lt {x)::: - J pex)dx , .sfi'J _ (p(:t:)d:x J L[(X) =: e /JJmh J hnz,fliJ d"JeJfI~jm.J~f1I!I)]MJ6N[jf1 5'llr:Jn3n .'Jh01J3J51Tl3Jbn ilJbtPmLJd.J.J {LY "+ /; y I ... C y:::. 0 f.,Jbn~ BJotfrnc 1d J UJe.JLr a, -£ (!J C (fl1:-0) Jm1J'.Jd':Jc.n hnlJlb3J3nJ 7 hmcm Y== H::r) tJdIJJdJC.n c.'J'::J5:jJ/IJJ.J· ClJ[.'fmodn& o-1rJ D.J3IJ -DnAs8. dJ'Jm'!3!Jt7l JJ& 'd.:J63ndau dn3trJ(J) Lub:J R3:JEn JnI6J[;fJJ dmlxlJDDmtn f1) 3J/;!Pn)c.i3IJL flrnaJ~n JdtrJ!i.XJMf) . .;JIJ/;.JOl3n0} Jr.'0JC hnJ'Jn 2113&lJ/(f(JIJ>j Am;} t!l'J :)1 fJ ':h Jnn.;!; JnLn J8mWl:J£f2Jn, DrncrT1 (16'.1 Cz hJfl8.J c?!:JedfJ3.JdtJ? d.Jf?r£ Y=C1.Y1.+C2Y2 JMJtJl3J nJIJi3.J ( f) DJrd!'JC"2d.., Ll.})/DJl:l£/l. d.JNfJC.JL'" , Jj I III 1/ I II (CJ 'Yri'Uh) i P(Cr"Yl +C2'h) f. q (U!r1(2Y2) ==edy, +P'}j .. rz')1) i- (2 02 "Ph f.·{Yt) ::: C l' () + C 2 '0 := 0. JJnL 3.>,7m, (OIf3Y"1)/)lt'IUCJM oJ5JPmo3nL ?JITIJJtYl JJm6.J6L1lnL cJJ5bJ'6C!!3Afon£'';o 2JJdmJenIJ.Jh..J, JI'I.ueJJJ > hmJ (!)'J 3ldm 3n(Jl ({) d_'&:Pmc:iJrJt fund.J mIJ Yt {'J Y2 t:Jdrrflj/:e.Je,x JJmSJlJL6t f.Jn·!lmJx{f)J dY!JJne:k}.;.Yu..J ;;':1&7/)3f»)~ J.J3f1,s ~ ::: CJ. 'Jj + C2 '12 (2) n:J6J6J (f) ?JJlilPrnc,73I1/" 1Yn3Je.n JJmo.:-IJUt1 . mMJ, !.udfl.:J"3.Jcfl 'bmaJ<Vl J:JmS.JI:JU;nL l.uDJ eJc"m-il'!e..iJ::JCfIJ A~+P';\+q-:::O (3) j3Jdut?Jc 3J£L.1Il:::.JO..l?L7, lJmd.JcL.llr (f) en'5JA2oifflJC:'JnlJ 3J;;l!moJn6 d.JOJti7JOud.JLn J.JOJPrnc::Jc,J }!f3n.;. :3JoJn onunm D.J 2n 'd1;](JJD3J3J: f) !JmU'..l 2JDJUnJ(J)JOx aJlJtPlllc:.J;UJ .dJ& mAI1 dJou!J3J3J3:;cJ) S.;Je3IJC/l f!3JL)(). .3rnJ3JOl, J10 C3:Jt3J6f1J /\1. {?J Ai. J.;'dn6 0'j/;jlfllJdn '::J1. ::(/'t T e.J 'Y co e ~\zX nj[;)d/UQ (1) a.J£!Pmu3nL eJ~/n'j;7e.i3JCt1 JJm6J6L£./c3IJ· dJIlOlL,) if, BJdrrt.:JJn{!JOCnMJ IJ'IJ.Jfl./)J, hJC'2J(J 'dJ'35h6JJ 'h::. (2 (~\-~) X .j!U.J 2~ean3IJ· 'J.nJdmlJ'J,nm, hmJ iJLMn Y2, "l" ?. ~ .j3d.JJ{(J03nL.J(JJE tn-/.;. :J~"3JJmS'J()1(J) .J/.;,dJilJ(fJ{f)JC?, YJ.-013niJ. /;JeiJJC; Y~'::::/\.1e/\.tX. Y~=~I1"'e' I JdntfmJ 2>JJdEji3.J y/'+Pj/+{l'Jl ::; ').}e?''X+ p~/l': Cf e')./'X= e)..,J::{?.} +P 1\1+1,) == e '1.'-::0::0. (J)'J 'j, E J 'Y2- U ';jJ3o)/JJ6m (2) tfrn::.n-J.::]n, dnJflC:. JM) , hmd .JJ ;) ~d{hb3J3J'Jn (() B()OJ.J!v;;:/'().JL~n a.sSdtn- CJML S/llOJ~ JJmoJDUi!J J.13I.J tJbJ I 29 2J MJ/f.) dJO.1lJNblJaJc ,!JJo!fmOd.Jt J:I.31J Jh(J)1l CJJt3fl. 3rJJ1!J.Jt!71.1U CJJuYJJ .A. dJ'J1IfJ (I) :3.5r;tfmc~nL mh eJoln'J!J!J62Jx JJmwIJUi/'; Jm2J3!/JJ:Jo ~'J5:/!I()Jan YI=e"'-:' eJ 'YFXe';l~- .Jd ~':JEjlYfl.J(J}J t!Jdrnjjfle::0cm"O.J I/OJDJJ. ':Jj3.1 ll'bJtYiJ flbfl!Y, hmJ Yt C'.JJ3JJJrrY!3rcJoL (f)-/.;. 3J!J3.1E"J7)(J!J hmJ O)-V eJJ:!JdJ!Jrn'!3nc6L Y2-L/. aMI.J :1"2.' :: X' e AX + XA e?X:= {1+ I\X)t? /\:>; y~' = {I-t- ()::rJ let. x + (f+ ;{x)" e}.x::: /\ e?x-r 0, +- 1\2~ )e?X~ (2~ t- /\2..x:J e?~ nJe3J5 A JhnL (3) dJStfmcJ{JnL 9JL 3n, JJnIfmJ '), 2 -I- P?1 f q :=.{), binon ndnu JJdm 7 Amd flJr JIoJ.rcq.J!llJln :1J1JJ/)J, JEJ/'CJl !JnLJD3.JeMJ' Amd ;{ =- i . J.f). 2'),+P~D - L'J.fbJ{lJ<fl (I ( AX )2 .... P:J2+qY2 :;: e (O-X+O) =D . JJhndJC'.1 JJ 4.1d9763,'73.1'(;/7 (j) a.fcJ!lIhCJ""JflL, gma.!C' JJmo.JDlI::L J:l622.1 fuM Y = CJ e AX + C2xe"X= (C t +C2. x )e"-X: 3) nrnIYJ JJb.;!Jn.Jf11Ja.x: dJElPmcJ2JJl.J JI1J:hiJ liXk:3KIl OjjbJ.Jd/): Jd dmL P~-'iCl. ~D· JC!Jb'n'J - f2 P .0 /fq. - p£ J ,r') 6mm = -""2 D::; 2. J dJJ01D3.J3.12/J t I) i3.JlitlmodnL rnh ex3rn'.13l1e.J{JJc Jdm6.XJf.£,L Clm2?,LY..:dJIJ l C9'J5.:Ju'flJ2n ~= t?CLX 5Ii,b:x:, C!) Yz -::: e ax (I)s!3x, aJhmo/]', 3J{}1f) e.Jdfh::af)BJdc.Jnd.J ifbJC'.JJJ ~ /)Jf?2JJtf ~-::: ==-t.j Bx, h.JLr' .J.!JJJ d:JflJnJn. (Jb3Jdnlb~dm(]7] hmd IJbn5n .JjJ.0m'!3nod:JIJ (I}-l,. ;).Jdml;'d:7d.) rn,),,3JuO'!Jnu 'Y 2 be.:i6.J ~7h01;;.Jn!lJe., JJntPmJ -hJ3J!:P.J!JfT)fll nan .JJ..0l-.JIJrnnu[l)3nt, dJdJLf)[J).Jt'? )/t -m3nL· (J3JjDJ.3J: y: 0=. (eax/SiIJtx +e ax (sint:xJ':=!1 e a -'5in!5Yt-Eeoco5&r 7 ':):' =.a.(ae(1~Jn&x+ g ea~sg:x) +g(aea:rco5gx-tl~5;1&:d:::- t?(1X((a 2 _S:<)5inIJx+2afy (oS f5yJ. J2nzPmJ :J;' + py: +qYt= eG.:x(ra;(-f5 2 ) 5iflf]X f- 2t1.gtDsg;x) r pe fa (t15IfJ S:x:+ g &5&1:-) + t:t eQ'S Ii) ~ JC':: = e QX ((a;(-!5'J'+P{L f-q)si!J&x + (2at+Pt)Cos&r). Jd aJdmwb'YUOni.J {J'YC(JUb tfmOlJdnL c.Ju.JJiljf)tY.Jdoe uJ.J,d.fnnunJ 3ft3JbnuJ> , hr'1J a Z-!/'t-pa -+- 1. .:: 0 2o.fJ .... p-!3 = O. (12_1,2 fP(uq 0(-;)':- (Ai-f~: d ~ )'-1 = ~2 _ 2aiJ+pB-=-iJ2a+p):::- C(2'{-f...) ~p)= 8.0=0_ :<, JJAflO.fe, JJ 2J:xlmb.3.1JfJn 0) oJGtfJmc:Jdnu 'brnJJe. Jdmo.J61.Ji5U J:/Ju UJbJ 30 co hndb 3nrrn ,:;1f:;An?JIl. JJJmM/:i;J{!!J3"Ju 0-1. + a 2. +- 1- an+-... ::::: L CLn (1), !J.J(!jJJY a1., a 2 , ..., a fl , , 5fdnLJ8n:JM EJ,f':Jf)Cn !J()JJ'D3.70n.), IIfll1'D.3f)(J)n J5':JAn3f1 n=r. ~'l!Jmf!'>:ia.J' an -L .Jlrm{!J :;J.J Jd aDj!Jn 3nIJ Cfynl3S~f) f{J3!1n. n JC!:']6ni!cm01: Sr=O-d' S2=aJ.+(12,"·J Sh-=Qt. ... {ht-···+(1h==L{lK, .... Jd 1uJJ3L :Jb('r) /{ci t! 'JdJDl (j) 2b:)M3()L j:;hdm 1Jd26rJ, LJ.J<6Jcy ' con12JA J Sn-L JfJmt!?.JdJ n - :::Infl .3:JMrn ~.J(]fl· 25JNJ3niJ .JID2JJ~rra.J. Jt'j},!13(J!J !iJJn Jl!m~.Ja.J Jd df{.Yvl2Jnu j2hdm 1aJ(J'1.J 2f)J~:J3!Jrnanl ~t!..'3.JAL. 07'1 ;) /fj!JfI 3iJ 3JJ?iEJnJ 5JJn , dJu ::JnJd.JCYl Jlfme:/d.J 7 DlnCfn 6"nbJ.Jc:!.Je Ja ~.Jdff)D3.J.3..afl .:JfJ - ;LJl)'Clc .5l~/7. u!J3.J 6.. f()!l.Je nmJ 3(J)iJj(J) , 35'.?!ln3nf., .:JAJdJ&n6J M2loJ3u ollUfl :J:JMm 5..JCh1J ;)fJ3enNndIJ!.J jJ>.'J;;~·&nd.JU· JJ'JJiJ.5eJJ:h (J)'J (n /jl)j),n3n :::Id2J.HYU eJ 2nun "5J3nJ S, d..Jdn6 e>O f1 S= lim Sh 'JE':J L:.a K := lim L aK . n-t-oo K",,1 n ....oo K=d 00 nJbMonun01 dJ3JCf1O?JCJ(); i) 3.5~3J/Jm(J)' ),(()J Jljjfd13 n £1 + i:t q ~. "+/]1. ?h'J... :: L_~i i-~ .g nr1 fJJt'.JU' I q 1< j, jldd.J~n.i t'J dnUl ~JJnJ £:::: __ 1_ _ ;lJAl1Joll, O?~ .3IlLuf,2,:JdciJm a .1rn 2 2 tPWC(] 1-q. jArniJlut(1nt JnI0.Jcn n If'J3NJL ~JJnt aJJrn1JJ013C'xn ~J;YCIl07 e.J 'dJ36n'd£.J307, AmJ ,Nn.'fJ / q. / -::.}. dJdnE lim cj.,fl==o, Jn3/)1!~:Jo()') /10-+00 5 I/m Sn -= lim (PH. i - qn \=- 81. lim (I-Qt.) =: -B t = /J",*co 1l... ""I L f-q I 1.-1 n~DO r 1-1 TJ 2; 3JJ:3J!Jmoh hind ;;f)!J)l/73n _1._ -/- _1_ .,. _1_ +- . + i 1- = r _1__ 1·2 2· oj 3·4 17{/Jf-f) /7=1 17!IJ+i) j!JJ65efl.f c:J 3nlm3m01 J(1/.,(1 tJdf1. i33J.13L 5 =: lim 5n -:.I;m (_1_ t _1_.,.. _1_ +... Ii) = lim [(f- 2.1. J+ ( .!- _ .!... J +- {_f _!-J+ .__ oj- (.i. _ .}~J7_ n-M> n..,oo /·2 2·3 3·4 nflJtf) n.yoo 2 3 '3 4 h nHlJ = lim (1 __ )=1. J. n..,co I1tt. 00 n+1. 3) df)jl>n3() i -1 + i .. i.j-. :: L. (-1) .Jh.J,) j)'fJ.Jt'!n, )uea.J5 J2 J5'.:jliflJfll .:)JMm 5JJOJJ dfid fl"'i e.J3htrla.JJ CSn)={l,{).-I,tJ,· .. ) J hrno.2G1U" U'DJC'n.J, .JAu j/lfaJc:.n. ~'J'::l5cm@ c. 1 bctiMJrJL .:jILi2J.JeJnOliL o.sbuJbI!!YuOn!.J UJCtJ:Jd3..Jc:.!fJ2, JfJ!}?23'JmML 'K>3!Jfl0 uJ{ru6XY17 0?3fJLJ;J.JOn[, OJJI)) !J.J5.J6n07 , dJ/)'t/f)J.5e dfJ//{h2d5, hmd j!lJoJ'e dSjhIJ3JJLJ l3J.JI5IJnJd) [JJJe.Jt3fJ {J}.3/JL1a.,-an ; f) d6'j/)fl3f)[' !;J~)){!}J U,JUlJC/l IlJlllvCtrk3fJL {f.JldOlm d5!JJv)JnL j)U.d....67kJJ ..vi ~J/I!J~3J3J" 2J tJ)':J r:. ad) CJ E B n :J),:;(jJ(!() db'jM3.X3n.), bmcm C lunoJ Mu'!;}!).) , aAj/7!i -=:Jk;iJdiiJ fl:/l)m.J£ n; f r}= 1 00 co 00 00 00 26jAn3:Jo/Jlj nSf{ln+fSn) , Cican ~.J' [.;;({Ln+Bn)="[;;.{Ln+-'{;;Bn . ~C~=:. L b CLn. 07 J m n ] d') (J)'::J d5~hfl3n .dl.xJJeJ)J, :JJ OI1D dntl1 fbrno.fef) DJ3!JfI !J~CJ)u .. HJ.b df)f)Lj)f,Y!3n:, . 00 eJJtf,;J()!.(.JdJ' ';.'Joe; 3yft3JEmo"), IJrnJ (J)'::J J/),3An3(J L. an jIlJOJeflJ, dJdl1/J I/m (Ln=O. dJb?JnM n:::i n~oo c:.mOl YJhdm DJJJJ() Sn==a:1 .... a2+···~a/l ~J 011-1:::: a:t~a2+ .. ·+ah-i (!J>i). Lr'bJetJJ lim 5/)=--5 h~oo eJ lim 5n-1='5, UJf..JiY S JAnL JnW'.JJ-:Jcfl d'i';j!Jfl3nL DJdf). ;)J'dflf) Jim (Sn-5n-t):::; Ilm'Sn n ~ 00 h -1' 00 n-. ()Q lim 5n-J. :=5-5=0· dJ;y'Jd 5n-5n-l""an . .J·fJ.Jim[ln-=={). n-> 00 tJ --> 00 tJDmMdJ cEJdtf.jnLY:Jd::rc.nJ .. tbfTJ.3J(Y7 b.J3hr1b o:YCJ7bJ:tJ£ Jnl£;'J~JaJ JhJJ lj.JjdJAnLfJ dhjfv13nL jhfd5emdnWO?3fJL .J.(]. '8"rJ c:Jd.J Joy.,fl.jn!.J ClmaJUI bJYJn ~J:).JE d/)fJ/.£Aj~meJl, dJlJIUJ d6-:JIvL3n ..I!1 n!JrniJ 3J-,:}"(lJeJ). JL.J(},)fJJ ~ J.J<3J CIJ(J)Je J.tb'. j.5ham6n~C/I J/i!ivJ?Jn: 1+- ~ +- i... fo··· +.i- +'" =- f .!-. lfbJe/)J. I/man=/;in..!:..... =0 2 ~ n ~ i n /)-100 /)-100 n, 3i ilJl:hJ2 ;;r;1N0n YJJ) :YlJ?J5en. JOf)u eJfJJcJffjnifJdcJ'e eJ3':1f:)3XJ1 UJDflCJJt!.'3e:;am fl.f p3/Jn'dE;rrdJ 5 -,X7I dfl/.-l1 3Jdll. i3JEJ3nbf'r:'}110'> .fJ JS'3IJn3f'i., j:Jfdm 5JdnJ dnat:J3fnl3.J (Sn) = (5J.) S2,;3! SVl ...) t?J dlJLn C'.:!b£'m J/'I1.J&1 j:J1J d fT1 SJJJ"anL JnJe:;3IYna.J (S2n) = (52 , 5... J:' -). lIoJt:nJ, lim 511 = 5 ~J lim 52n:= S, D.f/lt!_rbJ/f dmN!2iJOl, !}~ _' /)-n,D' { hmJ lim S211-Sn)={) , dJaflJd, ;;.Jmn:JL :lbM3 !J~oo 52/l -511 =( 1+ 1-. +- L +". +-!....- +- ..L...... + _1_) _ (1.+. .L... 1.- +- +- _L_) =._1_ oJ- J.. _ it +- _1._) 2:> n n+1. 2n 2 ~ n /1+1 n'+2 2n > .l.._ +- _1._ +-... + _i_ = n. _1_ = _1_. 2.n 2n 2n 2n 2. .j jjJt:.f5 !tid (5211- Sn) 'l,,' d/JC'J6'YCIl Df}OJJ~JeJaJT~,) JJtP;j/)1J'Jdb, hmd ~):JM eJ~./d.J all'eJMJ, J.f7. /l~<:P 0<, tA!Jm5n:J01 J5'jhnJn {3.J&lc.r&JJ. 00 00 (}Je5!)JanLJ 6nC!.JOfJ. 30?:!3JO'J, JOj!ll13Jdn Lan (1) eJ L. gf) (2) eJe:iM01S'J~j):Jafl.fEfdI7J n»1 /)= t eJ .!I1113Xfl 1l-0I31lL an * Sn. dJdfJ6, ot:J j!J:i3JenJ (2) :JS'j!Jn3(), iM:aJI!YJ f):/5:/dJ {IJ dlr3h!l3f}LJ'. eJdtFjf)lJ'J6J' J(!'JEn'd[mm {S (J~ )-1111) eJ (S <;.;') J -/Vl, ';JJ!.J.JJJJf)We, OJ e J (2) 2IijhfJ3:i2JnL j:Jhdm 5JJ01J JnJe(}}hn0i2Jn. U'CJJC()J. S;.;) ~ S~:),.) (3). /)JeaJIJ, Jnllm'antY/, jhj3JeJiJ (2) JC:Jh!73fl, JdnlfJmJ jl'l./tJJen fl:/b':icJJ JflM j2h~!Tl fJJJtJ1J 3n2v?hn2JoJ. 2n2eJ3hrr0niJ :JhJLJJtYndIJL .;':JU'IJOctJC() In!Jmi3fJL tf).JS.JbdJ t! .:JL 2ndeJ3hmdJ IJdb:Jd.J fVdI11Ldb03N:1LfJ. ;L2JfJ!J (]) ·:jfjJmc!1'Jnf., dXI1tY/ (5n(/)) ;}nJC'.JJhm?JJ ndS:Jd.J g:Jdme..Jb 'JJ,}muAc3!.!1C/}. (IJ dC'Jhn3fJL eJe.idfltTl/J.. 7 3h:;dIJJlJmJnL ax7 m (5~n) dMt?J3lvnJJ Zt,eJ~.J. gheJ~ flJ g:;JmeJD {)JJmw?Jcy.,'CI1 2n;;eJJlvnaJ jl), 3.rnJMJiJ/:fJ),J!J()L (JlJmNdnL ouli.JbJJe, hff7df}J!lU' 3f}U'ntTlt jhJJJtYJ.J. :;1- ~/1 £n'd£.J3L (I) Jo V jhn3nD Jkd.femdJL· h. e· 2J l!Jb3rihncmm dJ2JC()0111· 3,lt3J6m07 1 IvnJ JIJJ!vJ3f1 L 00 - i ..Jhl1U :JIlJ{JJl!!fJ· dJMJQLf, hmatr/l/Jl 3f)lff) C/I 0<> i n:£ h~ Q :JlVdJt:!U L -(-, df[j/,rOlJ. dJ:Jfl6 j!l:;O.5C!1J n:l,!;:;dJ JM:Jm3 J L -- Jf{:Jfv)31J11" (/Jalud. JC!.3()c'n 'i/:JIJ.xJ tl~tn/l~I, n-:.1 n(n~f) f)1JJ3f).J. Am;; ~mJ.Jc.n IJ. -I713fJL j " ~ ~) 1 Jdf)lfmJ, 'dJC'Jh:;lJnL b/ld!JnL 07J6JIJd.Je 1 5'tilJ8') n.:/S:iaJ Jml.!'.:J n'" hfh+f J:Jc!I 2b'JhfJ.3nlf· 00 jm'dnLJ cn~Jf;n. 30113JO'>, Lan eJ/d3n(J)fJ73h:BrulYJJ f' J .sALJdnJaL lim -C1j;;' = CI.. .2JC!() 6· = n=i. n .... oo {) 0'1') 0{ <: i ,Jnu./Jo:JCfl JCjnl13n j!tJdJe.tJ,) 1 2) 1TJ'1 c(/ i, J6':Jlif13n o.J&JooJ.J. 3) tYt1 Ci=j, J]J./3L J.J.JN3;n 'JJ[J01!JJE.5 '. fl ~ . eJ3t!jnLfJdJ. i.J .J'3f}C'mm (JLJO?fJ q, h(}lJ'D3(), hmJ <x.<:q<.l. ;lJ'dr/) lim ./(If) Z q.. .JJf7t P rnJ, J.JAnjjcf) n-r= f,m2hfle.:J.j d:df3'X:/1. d.JLMCe:JdJ ":1H7nc-rnO,JL!' -(;/if;'.<: q. li.Jec,Jb db~hfJ3f7l :Yl.JaJemJnL b.J!./lJOJ!..J y, tJ3DJL JnLn f)J.3A(J),J U.Ji.Jh':Jcn hJme1!Jn1l3nu '<I.Jff3CJ, 'lIJJ3nd07.J 3nt3'JCf1/..bJm(JJ, hm2 JL ~J!1morliJ.J UJ'J,~e:id.) Il1h?:LJcIJ31 [)mJfvJe....>D e.Jb'~i2J':JCfJ d.Jdnb an <q.I1.-':1/fff7on?JlJe.J5 eJ I7d ~J:ltPf)e.J5, 11m;} E q.n ({}<:q <: t) do:JhnJfJ _'/vlL .y,J /J-j OJI;>f)} '2.Jt:.Yu3nu bn:J!Jf)b 1J.J~::k!3Jc1,:J. eJJJh1JbrVT!, IJlII,? .1/J.'!;I"l'n (1'1;;.7.., .7f/1l'''1.7~~( /I :IC·,I,IUII/f'. :') .1,/ ;';:~I,1/,', 1.1'\.,.?o, (fJ') '/ 1,/1/,1>1/, .UflC'Jd", of,J'1 /)/!lJ 0(;' It >1; dIJJfJC.':/dul an >((' :.JtlYnc7,.'2uL , UJ()f!.JhJLI t:J3.Jl:!J3bf){YI: J/m ali i={). .J :lJt?J.b :Jill JIJYlf)31lb YJJdJt:IIJCviL J'YU'flCJd:JC() j()!Jrndi>L, dJ07Ui, dn:;I} n..;>a:> e jJtfJ 1 !JrnJ 2m ifJ J~UJ 2531v13fJ c3.. J<52k JtVl.J . 3) Jd 6.s!;ncnL DJR3JIJfd:::'J{! UJ.!xlJ),nun.J dm3f1.)JJ6mm mAn n!.r.:JOYl 2EJ:Y1fJ3!1L ClJJJc.fKJlrI, AmJ m!vJ3.:JL (JJ3f)/; Q:=' i, JJah,Jd Jhmn dJm2.Jbfl 3JDf]Ot:n,J. d..JmhJ .:j() .:Jh:;dJe.fJ. JLJmn dS"dv13X3I1J f L eJ L_ i _. 11=1 n 11=.:t /12 (d. =-i 5nl1m6.J Jm[JdeJ6.> LJ'bmdnCn ff'morWlu ~ - //m;yn= t ()JJm:nbJ3I1m)· n... oo fh.JmhJJ~ o:Jd':j{)l1.Jd::JOlJ. I e?.5c.J3a:JhnL bnClJlJn. 3m:!3J01, d[{:'JJfJJn f. CLn <9.ff?J(3~J3h:2xl.J617J eJ mdmaL li''1 an;-, ~d. n-:{ n....,oo eL n L"J'JfJ!;; 1.) (J)'j q<:{, drnU'JJ:Yc.n dDjAfJ)n j!JJ6.rc:nJ. 2) (J7'Y Q:>1, db:!J!JTJJ() ?J.;DI)JcJt:./).J 13) (J;':J oi=:...l , a3;d3!J LJJJ~3rn 'dJdiYIb3J3J· eJJtf,jnlJ'.Jf3J. /) .f3n(!}m(JJ nUtTln q,. nfJlJ'b3fJ, 11m2 c< < q < i. J,J'd()!i lim 0J~t < 1. .x1f)rJrnJ ~ 3.JfdJJ n-1OO a f) ':JUJ 6m2Mt:.J6 eJbJJ(J':fUl, ClJ!.Jl'JCL?JJJ ':1t:Ptrr<:mo.JiJ' ctn+ 1 «, q.. h.re3Jo d6'jn())nL ::I1JaJerno!lL .D.rlnJOlb J)" (1n 32 J/;CJJJ3lJ d()W bJY>cnJ bJiJIl'!Ja) hJmeJ5rndfJL 'JJffX.J' 'lIJa?:lk!alJ 3fl3':JcnLlJam(J), hmJ ;;t 'YffmanJJ LJIJ':Ict'ad..J jnl0X/l3.J £m31vJe..s5 e.J{)~Jd':JLf). <JJ2Ja and -<017'1. :Jilmal}"2(}C'JI) :33.J.5(i:J2JJ ~ a2-<arq.., a3<a~·q <a r 1\ av<a3·1-<a1.·q3>,.~., an<arqn:t .... hJei3JWLf 0.( q < t 1 JJmfmJ :J[Jjhn?Jn fat .q h .JMf; :ilJiJ.Jell , ;JJ')Jf)O an <aJ.qO-i ':!!If!1(.trme.J<J ., /l-:! 'ZJ:Je.J!darJ/; EfJ~£1lL mJ6.J!Xl..;e, e.f3.5f;=1~/jn011 hmd YJ1i3Je/u Jm1l':J(]::t07 dfJjnn3nO'. 2) .xl .'1J<lcnlJ?JJ3.kJn, flJ:J q hnlJ'b3/; J 3t7C'.7;;}m nL.7, 11m:! ()( > q ';> f, .JWonrJfl'::!M ;}/SIG71d()(J'1 In YI-. e'.76m, .0md (1n>ai·qn- t , /;.Jf}eJ./JJLf, a:!>O ~J q '>1 JIIM.,(J,JdrJ& dJ073.J01/j{n/Jj;]ot7J t'J3'://)30fJfl),hmJ Jim (lh "* O. .;jJe.Jb jn 1 J5"::!lfJJr]u :/JiJ.JemdrJ/'" J':JllrJcjdxn JnlYrXlnt dXMI , 3e"Jd':JUr!lJdJ, hrnJ Jrnu'JJ:J01 h~cP 3f)::Jhn:Jn aJ02Jf!!'iJ(p()J·. 00 00 i f 3) JJ Q..;bnCn/.; eJiJ.JlJJo':Jmidue. nO) t3Jb3fJ!Jncmm JErdinli2tl: L - BJ L -rj' Jc3!lC(] n= 1. n n=-l f]"" dJIJ..klm5Jf<J:J01J. hm2 mM3:Jb(J0nu q:::.l, JJ,])JJ~ hmJtnhl!' 3mJ'n01' .!nh3:Jcn dJ072LJ6n Jf,/l0 d.sE'JOetl, J:;rnA:; !In - ~.jaJeJ). 07.Jm/1JOJ e.Jdt1'jl7lf:/J:xJJ.J· (!!' JntJl)fIlrnL t1l.7m!lJJ.J tJn'J.fOJmbJlf KJ 25' ;'j,113J(Jl7u 2Ju.Jb.fa 011mhJ3.J, rn'J e.5e.Jof}{f) hf1!fD3!lJJ ((In) JnJllJ3fvndJ dml.JrntfJm/i:JI)J~ dflfMi'!ut!3fJL /)'X!ll.JJ:jJ/J, J1JIJ()/J 00 f]! 6ndJoJmoJlfY.J dbjhn3n ad. -a2 +-a3-a'-i+ . <0:= L. [-1) + an .JnflL :j!J'/3.5dJ. 17=1. B..5JtP~nLJ'.fa.J JJb3nbnCfl107 dm1YJ2':'J01 ;}[{'!)/v)3fl/'" jJMm 5.JdOlJ Jr.JenNrd.J {Sn h: (5"i , S:21 S3 St'·)' ;;{;e.; 3JfdJbmtfJ JJ JnJe :J3llfrJ(JnL ::IJ:k3.5&rk3.J .fdnuJOJ3nL !JJ~!YlUJ.J ~J-A3J&n0l,!lInJ JhJdu:1JrJ .Y:fJJ6 ;}/lJCJ ();!, hrr2JJdf) = {52n-v -:::: (51, S3 ' 56,"') e.J {S2n):::. {5 2 ,S.,., '.)6 ,... ).("'J IJrnd Ibm LPmOl (j;(!>3A2dn J:/3aJ. Jd JIl;:}eJ3hmo53flu :YJ-ia.J&nd.J dfl':JflU't:.1dJ 3.fl1:JhfJU!luLfJU O?.Jmf,J:JnL uJl!3~3JLZ:J. u.J!LJcl'?mdIH nJ,jJ.J3.J, IYnJ in!J3JC/1 JJ(JJa.J6n X:idJCYJ5 eJ d3XmeJE fjJ(jm/D~.JI607. dJrrIlJ 31) - v,t2.feJ) C?.J 'JJJdme.J6 ';12 2mLu 'bC.3k!cn. mhfl31 ')jJJtY7b?JJ~.J'J(l o/;?jJorJ(Jj .7htnwnNu, Jdn1fmJ ~3:Jf) 3Jf?325f!107 2/xn -:;l(f)/7 , dJ,]J C(/{fue- (52nJ-nL 1JhuenJaJ eJ ZJJmf:5D flJdmlJ,/oe:Yl:JonOJ . .f(!>£11'J6::Ycfl O1WJa.JdfJ dfJli(!'Ja/'JIi fan) JnJ {!.)3!Jm6nL jc:f2,Jem6nCJJb {hJIJ' (J7JJ/I{J JMn3 Je.3fJoe 2/1()f!.'J{J.J O1Jm/)J3n!.J ~!JIr0fM&f)) t?..J Jd !)()/Y63JJrJU eJC:.JCYJmrI1CJ()eJO. d.;hmLJif' S2.=~-a2<.ai (/iJeaJb [lA."){)) , S,,=.ara2+-a3-a.. =a:!-{an23) -a4<ai. (hseaJD a2.>a3 e.Ja'i>()) eJ J.:1. 52h<at. J·n· (S2n) Jf)Je.731Jrr,3.l '6J!Jtr1c:50 rbJfrll.J.loC1Yl'XT!J (11 hfWWI707. 1l;,e;670J jJ) 10& 2.JJe.JC/J (JJJ,0~Jheni3:iam).JEi: S" =:: ad. -a 2- {,~:; - av -= = 52 +-(CL3-(4 J > 52' S'" =O--cO,2 +(l3-r14r(k--~ = S'tt- (Cia -Ok» S" B.J .)·2. hsU' {J.J2DJd.J I:!morldJ& 11m 52/) =- lim 5.2n-i ~ nan :3JJrn:JC:f)E..Jo~:Jtnaf; S.2n= 52.n-i +a2h !Pmctf7 /) -t(X> Il.... co cmMfl-Jlj, tJJ'Y oJ3li073.5cnLf{fJ(j'.Jd07, limJ !JJC'OJ/;- 07JmhJdnL c!rJNndn07 I/m an =0, .JdmPmJ , liD JetJJ , hmd f1~oO lim a2.n=[). tHo::> flJJmAJJ.J eJJ1fJ.:jlllf.J~':fLnJ· GO SCJ[;mdtP:'Jh.se jl'd{}Jerr0J. JIJ!>hfJ3!.J Lan (f) J6meJ6.J JJ/.;mC.j!P.:JllJe 3h,:/d.;e/I, or:J .JI,.J2J.r en.) n-=- 1. <X=' 2nM 15'.J3h:JlJnu JiJLmc.':J1kivJ bnf!neJ.JanuJ3JIJ 'll~a.J6ocn JbYJ(}3fJ' :J.n. trtJ :Yl.iJJeJ1.J JJ":W73rJ L /:2 n l (2) . n=f (1l:JmnJ dJ . 0/') Jb~hnJn ~umd lfJ'JhH! j!ri(JJt:fIJ, 3J'Jn6 nL .fi3.:J'!JC:J6I>n3 ;jf,JaX'.I1Lf'J.J 33 {'J J,P)!lu'J6J . Jr!..' ?>f)fl'JEtnm Lin = /anl-t-O-n . v" =- /(in!- an 2 2. Je3fJOl 'J:;1JJJf,SJ3fJJ 1 hmJ 0 ~ lin ~ Ian! e.J 0 ~ Vn ~/an/. JJntlrnJ, IJJef3Jb JrJllm"2nL mJ!)J.bJ,;e j!li35i1fll (2) -J.r;j!JfJ3n, 'Jj~.sNant bfl'd5rJlJ OJ.JIiJI:i1re .1/iJ3Je/l fl:f!i.i3.J dSjlin3:k3nlf: r/.Ln e.; 1: \.In. d.J 'lJn5, JA:6.reJJ MS.i3.J JYvmJ:J f; (!in -Vn). J.J;3!Ud Lin-V,.,==llh' d.Jo.JWf:.)(h .1lva;; :ilJdf).Jd.> (;~ 1..J5'iM31J1f. f'lJ!1YLxJ.s 8;J 1I'~.i3:x flJ ?:Jf)f1:J3b,J' .J2 tJvmn:JdnL ':1.Jc,fdEJWOl e.Jd:JOd., .rtJ.J 1J.J8Jh(J)O}Jbn. :;·n· ~1fJ<Ic:k3.j ;}D';jIJrHn n~mlJ :JII:ilJen, dJ&~.XJ .L .~,_ f 1 i .J/I r0miJ .x:mflc!/J:P:'J!J.Je M13Jt'IJ . .J1J:xnIJJ 1 dJ2.JCfldlJ(J, JOj!>nJn 1- .2 + 3 - 'f" +..'. hmamhiJ' M.ilim, fJ2/} jIJfC3JeJ).J c.JIIJIJrJlJ7JiJ Ol.JffltJU d.JOuJ!, (?Jail.;,] JM .JJundJf)!iue:JIJ.Jd.JY) ];harr£rtY<:n JGJM3rib a,;£r<loemant &am. ir,hr r )2JMl j/l.Ja.r~J. nD:;{]J dD~/Jn3i3IJ, hm2oantJ' ~!J:iaS(l£n Jhnj;~-J~,3A;d-;h-~-~abnc:JdlJt> JIi:;'· (JJeDfl, JnhrMfl(JJ :Jh:i3Jen J5':3IlfJJ:i31> JD'me.i3.lm. Ja/.m:.'2tbh.Jt! .J!JJ3.se ;)5'jhfl3.i3u J~fJJ ~Je.J.an 25fl'JIDcm3J!)n (J]3n!J:kD: /h':J d)::/JfT31> .J3lJfiu::J1fJ:'JAJe 3IlJ JJenJ. d..!'JfJ£ Jliun CJ3IJ.Jdnb DJOn£dfJ..?!JfI (3Je.J£';~l3n/; clJt>.JJJe .!If)(!'YJ'jen !1lfjnn.3flJI' nd5".JCL 3!Li3JeIJ e,J dJ!JJJf n;3n3J !>.)In .7:J'SJ.dJ, hJU' <ltnU'..Jd5L db':5!Jfl3t. IJn33J3J, lim;} :JnlJrnafl{)) j!J:;d.!e JojM3.JoiJ Jb,Jtnn OJ3nL&J .;IJ J:l301· .3:hJm8' aJP:JIJd'eJo.;, nmJ hm2mYIll' Jh '.15e.s nJml S (hlJl!'lJ3n .iii .7hm-.Jhtnn +00, -00 1JnJJmcmm.J1JJlin) , 'lhndod.J ;}mJYJ<b07 JnlJtrlJnOJ jl>:J '2Jen 2b'J/1n3f1L 5J3/L'IJn n!.u 3.se.J3J!jjIJ'Jcmm , hmd 2nt!2J"(J'J01 dE:JIlIJJIJ!J .5JdfJ n!!llJb 9:>:J/;tP,J e S. 'I 3 00 n O-O+-D..i:r.+azYi-a3X +-- - -:- LanX (n rr=O UJiJ(IIJ ;;/ijM3L, !.JJe..J1J' ao I al' 0..2, a3 ,... JmLJ'J,}:Xn f,n.lf6.J:;Jn:>, hmdXtlJ,J1J' Jd 2/i:JhIJ3n!J :JmY!3f1lf"nJ5 tfi3n f:!:,nJ(J), X jn-!J'3c.;en , bJnnuiJm3J6n JlJ'j/Jn31l JDJnt!.2dJ. co n (i) .J5'Yln3!..J JD'me:/2.J :Lo f).Jlulhc.drJ jldaJen, m':Y :JI,JdSeJJJ hNJ'D3ntnn (}D:Jhrl3n Lan:r 0 fl::: I ' ~·:IJC.J (7;] !J..7!>J!1JCiJJ.J !JfldM30iJ, hmd.Jc'J()!f .:JhfJ.JeJJ.J lJ.Jhfl!Om3.Jb(l dC'.!/Jn3fJ, b.Jhnf.,bIJ13JM ;75' 3IYJ]n!J j!lJdscMnL LJnJNJCJ :JCme.JdJ· .Jm3xn b.J!>nMfI13.:/Jn dDjhn3nl :5hJdJeirKJlI.!J 1JJJ2lu3o Jh.JiJ'.JtYuCJ)J, hJe3.JD, U'b.fC::.fJJ: Xo =0 t':;Az!hc'dn (f) Jt'.3IYlJn :5IJ2MeJJJ· /h'Y M:am!Jn b.JfJnuJ 4.7l1dod.; l1~b 6.:1JnUtn3JI)I1 db'.:M!YJIJ j/L->llJerr¥J/)t LJfJ<}!;J?JO - J3niJ eJ(!l:JJ&'Jl ldJ:YJooJo MCJ3J .f d ~ (!!' f) /; dJl.J1t e.k1tPJ()if:Ja':!t:n 'd.JoeJan i7JrnA:JCJ.J. 07'J D.;An!Jbm3JbIJ dlf'3M3n 2kX3.JeN Il.JM_7 Xo *0 l5)htIhdJlJ, d./onD nl> ndli.JaJ JA:k3JefJ (j':)/l(TJ 2.JHhLf, - n2(j',JaJ .0fJlnC:fl?:J!lJe :Y'J.i3JVl) J3X.J nL..707 X IJ.J/ltffJc2IM; hrndc-n!.Jtl!3flIj,Jff Ix/ -<. / Xo / e;2JJ.5fJlfJOJ. (J)':J SC3[,n'J6JJ(Jl q ~ I x J 1 dJ'llNl W.st2./IJ. IvnJ !q 1<: 1. f,.se2-_JE, .Ifl!'JmJflb {f)J 00.. IXo! !5.J6JJe, dO":JAn3n L. an1:~ .)Ml:JILi3.Jt!f1 .Jdf11f>tnd .:lNJI1 ~&J t5'.J3IJn &'::Jcl11J.J.j:Jlj dnnLGIlJt?Jf1IJ· (lJ'j aJ3fl n-o n ot:JE.J'dat ?fldc9:J3)1In2nfJ dvJJeIJJ(Jnu J'jLr'fJOdX :JnI>flk1Ju , eJ3Jbj3bfJ/J), hfl7J fa fl T a ) dndt?.J?hr0J 'J.JdlTJ iJ./lJC::),'XJ)J' J. (). mAlJ2:>dIJ nfJJtJin .M >0 /inu6Jn, !Ynd / ah X:/ ~ J1 :JmJ.2Cf] 17-/lI3f)6' 'ilJ1>3fJ<kIJJ enl;:;!r))Ol hi J hJ (/XI)n I fJl h IJ n lanX 1:= anXo .- = O-nXa/·q ~.YJ,q . !Xol 00 sj:;eJb' (J)'j 253nf:J...J5JJ(]?, hm3 hmlfJ I q/ <. 1. , dJ'Jn5 JO'j!Jn3n L J.J, qn. j/u(JJe.IIJ' t?JeJ'df}ff)/['J~f1 J.r.:WJ 11=0 00 IJI Jilt j!J~Jernd()/.; 'dJeJhJdnIJ bn'J£nL Ld!3';)d3..?c..£J e.f3JM3!J!J(!J 1 hmd JIlJaretJ IJ:J'S.J(J.J do':;"Y13fl n{;i; Jan'}: /. J·n. (f) 2/J"jllnJfJ fl:!(j'J3.J JdIJmd1fJ::;/Ve. 2MdSeJI X b,Jlllfhc1Jl1. 07JrnAJa.J eJ;;,p.:j()IJ'Jt3~el1.J eJo'!pjnlf.Jd:JCfl (J)]m.!JJdM.Jb o,J(]mde.nli.JllJrMfJ. IJrnJ hJnnMm3JI)fI :J/J'!JM3flt ::n:i2Semd()L !m8llcJ3C.Jb ,J.73!.J !lIJ fJJ3nD_'13J' nm:J fl2n ITIJ3nIJ 5JJnlxJnJh o.Jl>tlhcmJ5 .Jndl.Je 1l.2flil'J3b UJtn.J3:J1J(J)Jf} ':.!f!3hm JI>onb J.7m!!3 !/?LJO fDJIl-fnr:!.J. ilbJt!n,) .5LJmn 073nIJJont J:/mIiJ L,n2IlJ3c.J:Jdfl .JNJJ(j' :JlJmone 'd-.12eJon bJbr>L, hnut'J3IJthfJ 'd:JJCJei3n: 1 3~ (-r~·.F~,), [-R",R], (-RiR7 eJ [-RiR), UJeJIf O~R~+oo. JlJJ(J) R-f., JlJ'meJ13J b.JnnL.i:fn3J!;n alJ3IJfI"' Jnb jlddJetr2nl IJJe.m!Jn. eJJf1Jwe.Jd.J' .JilJJJem(JnL !lJeJ)~Mh e.kbbJMJ07.JO.JCn 07JnfJJdJ f)!J.JJ, 1m:! !;nufJ IXI < "-R J!f'jP,fl311 :1-VaJ8'JJ , nmon NniJ'J Ix I;> R - J8':Y1I13f1 l3Jo'llc.re'JJ. bJJJlJt7Jtf}JI5"rlJ 'd:J<:7t?:Jon In. 7mlu ~ m':J J!llJJdfl/ClD II rn -C/i (1." I 7 d.JCJn(j (J) /?1J'.1IJ/)]nI, .1A7d.Jt~'mi3IJ!J !U(!II,:/LJt, {jJ dlflllOl3C:J Zf.J 1/ .... ou 1. I;m~ /1->- 00 lim -v;a;;;} n~oo n/, ~ ?>n/.; jm(JnL 6n';)"neJS C'J d!!jhn3n!.J jAJd.f<'!.rri3nu .tJLJhc:Jdxn Jnhm"Jne.J[J: .fnh3:Jc 'llJ:JOJtJ3:J3./Jn lim l/JanT"/<l 00 n4CO J Jdnt!InJ J6':JInYl L.I t1n:J:.. n I /l :/liJdJ jl1:J2JJetI .:Jln~ lin'd£nu tJ7J1i.;MJe. dJ::Jflli .:fu?Jen ndl.ifdJ (f) ,!llJ':jM3nff. /)=0 ):;rrJu 2Jdmb3J3J on lim YJl1nXf)1 ~ 1. JAJn!J, l3J!JJ3J::JclI D!nJMe.Jo eJ/;:;:j(]jcn 'dJ!JA'Jt{l2dJ ::;J!1.?Cn73JIY: :) .....0 1/;a.,X. n j'>l, wnt!Jb.JU' /llnx fl l>l. J:lJC'J£ :YJ U>bJeJ)J ,hmJ I/m lt1.nXh)~tJ ')'JLf' do.dJn3nb ~ I)~oo J'JuJflOd2C/1 irwrJnu dJCM1 !Jn~tS.J3fJ ()oJ/;' M:! (f) d53hfl3t1 aJ6dUt!nJ. e;Jr:&ol/.iJJ· uJ.JiJJhl1!..J/U 3J"t3:Jbf11(JJ. hme? !;rnU'.J l:Jc I ~ j Dmon hmLJ'.J Ix/ > ---::n- R-::. 1 lim I anH! h--'>oo an 'lJ.JDn(]?:x!Jj. j!J.:Jdfen,Jd ~:Y.fCJt?n1J 6mcmcm:Jdfh.J, :J.(). X =.-R eJ X-=oR b:Jlu/hci"6'dn D_'fJrlbn?J.JEJn 'JJndci2JJ 10mfJ jll:;;3.Jef} , i(lJndoa.s 10m/.; aJo90ef} C'J ~JfJdO& .JntlJ-.Jhm dJ07J.JI.i(l/1 njmIJ fltJa.ft?f). dJ rr:MdfJ jn 3JD2J::Jefi. J!.J:Jf!ln df)j/]n3~6()L 2Jo5Cf1cru2rJ..J; <XJ X n ;=- n ~ X n L.~, L-X, L--7 (J-:=1 n n=1 /1=1 n shJJ dE.xn CJWe2,Jl)fI, hrrilJd d~fl!J ~i3JenJ-i ~~JC.Jej(JlV. 'd.JIJJ"J.JJ.1Jn1JJC?, [-1; 1Jd-1; I), [. f; j), (- f: 1]. ':J J[jf)dJfjJ. 'dJndc.it3J hJ!J!lUJrn3J611 2S'.3hfl!Jn ()Jmb :JNn?J.JetJ JDmcme X == 0 OJhtf>Jc8f) , J·n· R =0 (Y.J 00 00 t n JJJJa.fen (Jj/,/!J 2tn:Jc:.L (!' -.JAdfbJ, J.(). R =- + 00 . JbJouJn.J' dJiJ.JCfl07.Jt3' L tI n x n e.J L - n fl X d5M n=1 h=-f 3JJn, d.JLu(JJdn!.JJe. 3rrd3JOJ, J!(X) "3':Jb:ILJ'fJJU (l l5'.JhJfncn/.; lund::; JnC'.JJm'dn dJJ!?[)rU 5iJ/J1JofJJllfiManL 6'.Jhan:i3'j.~/CrJ. JS'dY13L ) [11/(2) ') (,111/ :> i f [{aJ+- ~ (J:.-(L)+ _(1- (x-aJ'V+ ~ (X-{lY't- .. (1) f: 2; 3 ! J6mC3.JdJ f(X) (ly:;[;jIYnnlJ Ibncrn!Jnt d6':J/Y13()· hm~:J!.J..;!.J' JL 35'~3fl jh.J(JJetJJ f(xJ-jJ/J) .J.(7. nmLJ'J I i" flii/ ) f(J:) =. .j({L) -I- f raj (x-a) + --.!!!:!.. {x-ar -+- _la_ (:r.-(JJ~ ... . 1! .2! '5! . JJom?ufi, 11m;; '!3'::!£.1LJ'flJ nd'c.XJJ (J'}J]nIJ tf:Jncmhnb ;}S'3M3.fe. -R3JIin dnfbJlYlu t?J3.JeJfJ!jrnm OJ':) hmeflbJ.J 35 BJUJd3.iJn J/.L}(J)n 3J2lJ 0 .k!n!.JJtJ73fJL Jt!:3[;n'J&nm SfJ (X) -1m (f) JIJ'.J/)f)3fJL f)-::;hn 3.Jlidm 5Jdn e... 'd:;.3 Dn;)Sm01, limd dJ~nS f/:vfj!..J diU/) .leA? C?.JiJ/J.;3CnO) IP.JnCmlint 03mhd!:JC.J 'd2ndCJd.J -f?.. mD.JNnU JiJ.J: f(xJ=: s'1fX) + ILn (X), lJJeJiJ 'C:n (X) = f(M(O (x-a)'} (c 2fT}(J)J3uJO~cn..) a eJ X 10/ufncJ9u til omMuJ J!V)/; ff.JfJCrrVJ()f, o.3mh3:Jcnt D.J20?1J01n DJ3M . .J.:f.HlJD -t.Jb!.JJ hmo :!(x)= lim 5/){:1:) JJJn!5 (!j /)-> 00 dD(7J{(T)e (J.J[JfJ6' I NrJ/!'J lim 'In (xJ =0. Jb':;, b!JJJIJ.Jnlve limd 3m:l.1J01, '!J':JD:JlJ'nn!.J d"0CoJ tPJIJOnhn/.; d5.ffin3Je: n~ {!J!J.l'J 3}31JJ /lJ 2 n6' {!J J6mone JJ df)fj , IJrnJlJ #:J nc;rv{nu '?3mNlYclJ!.J (jjPlt7Jll07/l !l'J3M 5::x:nLtJ3.JC J(}!JLIj 1L./3nL. hm,rJ (2=0, dJdh(j (/) do:YY131J JJ.JanhJfJnL Jt'jMJfJ jj3!JJ .. Jd ~ (2) aJlb dtJn('}f2Ju UJ6JL f(X) -= f[O) + P (OJ .L + pl{O) x,z+ fltl(o) x~... (3) If 2!3! . (JJ03/)tJnundJ (JJJJcnI!JJ6f1. oJ3'JJc.rnm (7J3c:mn1bn U J5~fl3f e eX, 5inx, CtJsx eJ En (1+.1:) OJ'JIliJ/fJJdn· iJ f (x) = eX. ~.J!J dJ3nJ.})JJDnm 'In(X 7 lueaJli 1- (/}'rX) == eX, .fJn/lmJ, 'In (T1 == e~ x h , !JJeJ U' 0 n. C Jm{Jl.d1JJ(J~cnJ 0 t'J X-u 'dmlvlL e.J Jt1fJff'mJ e.C~el':;cJ. /l}':! Jf3IJOJ3JOJ!.JS'fJ,0dm, hmJ f:)2l3nUny.,n x 073nu lim X!7 =.D, fl.J3Juj36W, lim] /'In('X.JI~ e IX /./x!'L-+ O (!7..J>OO)' Ll./JJwt?Jd.Jl b"fJnL3f1J!Jn !I-H)::.J n! !7 .1 X-073fJJ., 'J.JCLJI'4c:nJ 8J3£'.J/J/rJiJ1 (3) f!JI17CrMJ ~ hm;]JcliJiJ' f(()) = f{tl)({))=:e x / x =o=.l tPrn.:mJ.Jdnt a.rJrn .J:ifjf6J /;.J6) x X X 2 X;' e :=1+-+-+-+'·· 1~ :<! 3! . hml/J X -=,' 1 (J3.J:JIi.JCJ.) 2) fer) == Sin x. . ..JJ 'LJ(J)63J3.J2INY Je3fJCflJ ()iJf)/.J C!~O.JIJJ , hmJ 6JJnuJnJfln X (J:;IJJ!hC7JLJ.J mJfJL lim Zn{X)o=()· hJ~J.Jo }[o)=sin:xJ =0 , f'([))=C£JS"""/ =1, f''(O).:::-S;/)X~ :=. 0, n·~ C IX=Q UL.f:r=o r:::o flilro} =::-(j)S'YJ =-}, :i/1,{O)-=- 5if1x l -=-0,·· .. ' 2.J.J:/6JOJ "'-IX=:> IX=oD Sinx=x- X 3 + xo _ X "1- + .... 3! 5! "t-! 3) f (XJ = C{]5 X. ..JWcrn£3n!:JhJe dfJ3/l(!'.J2d1, IJmj X Z x~ x 6 CtJ5X -= d - ';l! + L;T - 6! + .... -f L;) j (X) =. Ell (It x)· Jd :iJJmDJ.J3JdfJ C/tP.:J()!J'eJdJ. hm;} (3) .rPtnCrno.J UJdJlw1I:TlJMJ OJ 'dnb~. !Jfl7!flJ XE:(-j',·f]· hJeo..J£ f{o)= £;'OrxJ/X=-<J={) 1 f'tO)=fffXr1x-z.o=='1.., fl'r.o)=:-{ffX.r1x~o-l, 1lf [{))=:{. '2..{It-Xf 31 =1-2, j(V(tJ):::.-/o2-3f1f:rF'1. =-1-2·3,··" :/(/}ro) = r-l)n-J{h-f)!(ltxf%:::o /X~Q x=oo = {-nf)-YI7-J).', o3J:i6iaJ hmtrJ X =1., )(»)nC'm
1/--страниц