5Cmt1s - Name: 0W 6v» Perm No: Section Time : Math 50 -...

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Unformatted text preview: Name: 0W 6v» Perm No: Section Time : Math 50 - Midterm. 1 February 6, 2007 Instructions: 0 This exam consists of 5 problems worth 10 points each, for a. total of 50 possible points" 0 You must show all your woxk and fully justify your answers in orde: to recieve full credit You may leave your answers in unsimplified form, unless the problem asks you to simplify I No books or csicuiators are allowed You may use a 011e~sided page of notes“ 0 Write your answers on the test itself, in the space aiotted. You may attach additional pages if necessary. 1. (a) Commute / 3:132 dn: — Bxyz dy + we!” dz Wham C is the Straight iine path from C (0,0,0) to (2,1, m1)“ C MS» m.d~v‘\c, E-c‘tacd‘fimt ‘22“ :31: OEtiT‘t "5‘7 SSKQM.“1K‘31%+X€:§EM 1:“ c’ ‘5; l w t} 1 g SUNS-24,13 “ l(,2t][£\L—t)~\ 4‘. 1t ed (A) M D (b) Is the integra}. in (a) independent of path? Justify your answer“ TM-QAAJIC Wei Cam» \an. wr‘IHeJA, M SQTDQJ; KME (Ar— 3x‘w mlxxjaj + w; k. SMQ. 0km VQW me; We... mlR’S chm \wéwwi. m waddA-mmuw <29 WT\L-a\r_p%‘ “‘ L. J. 1 a H A Vavgt WV“): \zfi: 5%; ""5""; :Qaie +1763» Jr”- N1" “1501?: Xe,“ ._3 % D W W \w‘xw (g wit“ WhMtiquWJ¥ 2 2" Find the surface area. of the sul'face S, which is parametrized by 32(u, v) = ucosv gb(u,v) = y(u,v) = usinv 2(u, v) m 1 ~ U2 for-all(15,11)withOfiuSlaudOSvSZw. SA 2 amt/w Rm We, E: >9: + ‘jf: + 23:: Law-v + swv + (~1MD‘L:I+ L/ul» (3—: x} ¥\fi$’ +31}: algtnlv + wva +0 :— UR" F = XMXV ““ \é/Civ * Eu}, =(W V)\J\L“Slh.v)+ (vafiuceév + Pauli) :vflmgv 'imv + M- (ASVKMV 1: 1m; \ ‘5" Erik/mg % JLHLMQML Am am 0 0 ._~ g” Um- §lu oh 0 1‘: '5‘ [raj— W:\+L~lu1 :8 &%JE ém clv Aw 7; W2} \ - 2. UCQUK S fiaw .. 5”“ L291)?”- 0W 5 is 3 \ : “gm—«o av -—- ESE-A) 3. Let S be the Sphere m2 + y? + 22 = 9 of radius 3, oriented with the inner normal 11. Compute f/xgdydzwgdzdngdxdy '5' ~41 iP¥=J=x1T+Uf~3 +1‘L) 33 XL &tfiAk+ K301“ ng: AX «FELM 5" :mw vss m}.th “S —— We“ {2. f“: W W 804A X}+Lj"+%} 91 M \NQ. wags} ‘HML WLMUS ERIE/h “Sn/«A, 3 TS Evian/M M m “MAM Wmvmflv‘ Sgélx +3.3 +0.1} (SLx &uj 5M7: =1 3 2:18“ Sm C(fmesmefi+ f3M®SMgf+ fem Mfg-3mg?” q 099452? O z“ 2%“ STE 83 WRWBamflE *ngl®<;\v~?htyf’> +~ mfififimqm A? GM W __ 1%“ \‘h 9 “map + gma gmth 'K'" LmQS qufi>&9 J?! T‘ rm; ’L’W' ,__ _ ... Y5 ‘ L S I. [~7(©\ 0 + in (h’IQSQMSfi _ iguam flay/6510+ WM}; L ‘3 W D O m 31 Cm mtfi‘imé 4% = 3W" Fgflfz 81T('0“03 316;} 4.. Compute jg 2332 d3: — 2yz dy «Jr :1: dz, where C is the curve given by c $(t) m cost r(t) m y(t) = sint 2(t) = 8111(213) + Sint fox‘OgtS 271 we, MAL Skw‘ Ww-mfl "UM. CAM-WE. C/ “M cm, 'erL Qwr‘rpmu‘, “E: 1X3 +Lj game, at): film (it) + {m t = 2. text <1th + Sm. Jr: t" 1 WM usUc) 4— vibe) ' WM; C/ TS W 0%— m 3\W&'O\C,{ 8 34V% L343 m 0% EthLfi-k-Lj Guru" m um’r «La-m x‘LHfi’LsJ (gum m um? {um ca m Lch—m‘w 0‘3- W MVL Ktth szgi'wi: M 1% Abra/Hg mm C, On m Way WW.) A w...) A d .4 .4 — 3f a It. L? F: R‘XEt “luhij +‘AL, WKLFB~ Bx Dy 0% =- 13) "(3 +(1xaatjj 1—01": ‘9’ ghfir Ag = 882423 ck“; viz, + (1):" DAEM 1‘; BQNX'“ W gbgiu-D 1.2:: + 3 figs :1 Swlbh‘ga -[2.><~1)(1X+0 014‘ Ag; ‘3" [H HLXfLMjI) okng W?“ X1443le 1W 7...; §1W8\(1“Lfr1)v&r009 =.—. 5g :3» w]: 00:) :Sum“%rfi©=@ 0 5. Let S be the top half of the unit sphere (file, 5‘ is given by $132 + y2 + 32 = 1 and z 2 0), oriented by the outer normal 11, and let F be the vector fieid F(a:, y, z) = (a: + ye”)i + 6ij + (2:2 + y2)k\ Integrate / / F~nda. s W» R is "HAD. \AMHL- CLC'SLL KL+L§Lél ‘m W Xfiheimt w R M a 3N We”. gm. 4m- tum muwfi a? M EFAAWWQW rLQYCmHtkL+KfiL¥ELS\ ONL 17(0. m m Amp M5} «rt m um} \MM. : gm 8‘ reroufjua + Vb\. (-H} a SWE‘LOIB» ~3— Vul (M) "1 g; + iLE-QJTUUBD 5 l 3 "J ...
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This note was uploaded on 04/07/2008 for the course MATH 5c taught by Professor Roche during the Fall '06 term at UCSB.

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5Cmt1s - Name: 0W 6v» Perm No: Section Time : Math 50 -...

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