solution12s - Name& ID Siam 2:00-3:00 Responses Without...

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Unformatted text preview: Name & ID: Siam 2:00-3:00 05/01/2009 Responses Without work will receive no credit. Each exercise is worth one point; the second two problems are on the back Exercise 1. Use the parameterization r(9,¢) = sinqbcosGi-l—sinqbsinflj +cosqbk, 0 < 9 _<_ 271', 0 < 4’) < 7r, to calculate the surface area of the unit sphere (You probably already know the answer but the Spoint is to do the calculation.) AM ”5| :5” mundadcl {‘91: -wtmll'fl +M¢mao + 0T5 _ - 5? a : omqi'coeé‘ii- +m¢ W93 ”MM“ ’1? :-=2 '3 j 'l? 7 _ t . __'_--fi Wm? —’ ’mftme Miami} (9 :flmzllwe? +03 ‘Wdlwol’wék MM mtwe we «mimosafleoa ”me 2’ : ,w Wéwg rm}: 9 'wefiéwmef + Mme . : Mewawe) + We} (0:47 ma +M1m1¢ MATH 53 Discussion - Kaspar ’143M957 ~M¢W¢t Exercise 3. Evaluate ffS zdS where 5’ is the portion of the cone 22 a: a: 2+1!2 betWeen the planes 2— — 1 and z — 3. ‘ WWW,W:W Sr. film93~m°°9lr+uwc93 Aral: MEI—“Rm, léblé?) TLJW‘ r11: WELL fWéj ‘4’ IL 1739f “Mme? +Maflé‘o +0): _,, 2 r )6? f .1: '3- k ' . , ' ‘ a [A 9 ’ 0,939 wfi 1 a 0-5: “mejmc‘sak -We W19 o .wwa'fi “was 40-31; '7': aumei’l—MM‘QS’ *Ml‘” ‘ .1 .2 2. ,_ 1 ’ 1 m Ola—We) «We +1 <- a :> lmerelrmanu W10 £243 ”Bahamian f“ 3 MMQJMdQ ’4 fag]? \JEMIQRM “’- 9‘“ \l-E—l %u?jh:l3 .' 2? XTT \JE 7% 03"” : 5211a 3 Exercise 4. Let F = 9:2i + y2 j + _22 k and S be the Mébius strip given by parameterization r(u, 6) = (2 cos 6 + u cos(l9/2))i + (2 sin 9 +11, cos(6/2))j + usin(9/2)k, 7—1 < u S— 2 and 0 < 6 < 2% Evaluate ffSF- £118, or convince me that I should not ask you this question. (Hint: The argument “Because it’s Friday,” as persuasive as it is will not earn the point. )- ”SE A? mmWWMW 5 are ...
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