MAT318-QUIZ2 - MAT 318 Instructor Mike Wang NAME Arlswg...

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Unformatted text preview: MAT 318 Instructor: Mike Wang NAME: Arlswg ‘46] 11/21/06 Quiz # 2 Since this is a take home quiz, grading will be strict. As usual, you are expected to show all work steps clearly. You may use any nonliving source available (books, intemet, etc.), but you are not allowed to communicate \anSWers with anyone. Live with honor! 1. Evaluate f :2 " 6 C 2 dz, where C is the boundary of the square with vertices i3 and i311 Z -— Z ’ . 7%‘5 .. A, + E...“ NEE. ace—z) - '3 1"?“ Ace—z +5-1— {Airs-=7 /7 _ .- ECE—L) —z,¢1,-.-~ : (A+B)%+2,A =>Azg EG-Z) 23+B=7 => 13:4» s 4 (Ci-Z : ch'E + £-L>CLE \ . \ ': ’3 got-22h; 4? 4§c%'2 ,, » L=B= “cm =‘ “f1 K :12) J ‘ More: Lia?“ = {if = — t’”: e be H)?" = -— [xi—\- uteri — cart}: @451ng =9 tMfit‘m‘] = - 7403,, 2. Evaluate §C1m[(iz)2] dz, where C is the unit semicircle in the upper half-plane about the origin. (15pts) Nora gee = xL—a + quQ = cos-k «mum: , oat e. t: J HEB-E 5; IM [CitflAg = § Hamléeackt at»: «MM-mi . c Q TC = S - lus'kScht' (—sivd: + Loos-Q cl": 0 ._ 1T _ z . a \ : S (2954:9ch — ZLOaS £$\wk) ° w o / m 2 2g tome/flake ~29 aces”:th At " .. mined ‘7 x” / ween K ta- ufcos'k tnflu‘ MET: utishdc t:o,u=0 du: *ffiw‘iét tat “=_\ 6/“: ms-kd-k t-«guv—o —d“=$\v\ké4: ’ 3. Find the Taylor series of the function f(z) = Ln(1—z) with center 20 = i. (15 pts) Nana: LWU .45 a: Lab -— (2:4,) "L—X ’ WM : LM [0—1) ~ 8-4)] : LVK L) I {J ‘ Jconwe‘m : MAO-O +~ Lug} ” Hi \61 : L‘AU- + {fink " €L%”L)] Do I h»\ V! ‘H-i ~ M ~ (Max) +, E 6W") 9“ [Ewc'ql IA Wm“, $4 \> A Fprcwfl 0F DENDM- fl \ 3 D -3; m x q. . é. 322,4 = Q ~\7(2‘+ 4H4) W = CL—OH; HA7" 4. Find the Taylor series of the function flz) = gig—4%:— With center 20 = 0. (15 pts) Z Z — k ”>%Z’+-\'$%H$ A + i + c #+-%z"-4 ' H j Loo = (Q—D (ea); (%+ 73’" AGwAz-r BLz—QGhfl + COL-43 7' (at-0&3 n)?” Azzmmwuwfiey —U§+c—2 —»C u; " (%-\)L%+ 737' (M @721 + HA+3+CJ$ + (QA—Ub ‘Q V Car—0 65+sz 2+1, (2,, \ \ o 7; L. \ R _' . * o '5 -\ '1 ~ 9.2 o '5 —w H 39/94 4 gem-‘ng B=-% “‘2 “ 0 ° '3 \ emu": 3‘ A~%.=39A= /4 W Wwflh um _3____;m,_; \ : 3!. {:7 q {+1 3 (-E-sz‘ \ I}? " 4 04:3 “ 04%.) 3 (1+9 y \ 3: V2, __\. yq’. ‘ R ’I (143 ~ " hart/131 3 [Hg/z]? - “'5‘. \ _ E ‘ .1”... .__L ‘ - OT (“at ‘l (Hi/2.3 ‘7- ("fit/7Az w —z 3\ °° “-£M_“ihm-z = EVE} quMZ) '1 “ M a M a \ “(—43 n 2. “2% ~“2 _ -E "M' “=0 qn=o 2W‘ A—\ A-tg “ - . m -g;.,.\_\\ L g“\ —%$?Q\ WH\ _ K—Hx: \ wocse \%\ < \ KI "V‘r mws o: cmdx’pumJC/E‘, ...
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This note was uploaded on 05/05/2008 for the course MATH 318 taught by Professor Wang during the Fall '06 term at Cal Poly Pomona.

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MAT318-QUIZ2 - MAT 318 Instructor Mike Wang NAME Arlswg...

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