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solution1s - NamegzID gm 200—300 Responses without work...

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Unformatted text preview: NamegzID; gm _ 200—300 05/08/2009 ' Responses without work Will receive no credit. Each exercise is worth one point and the last two problems are on the back. EXercise 1. Write and label the formulas for Green s Theorem, Stokes’ Theorem, and the Diver— gence Theorem (Just the formulasm—you don’t need to state all the hypotheses.) GWSQE F-al’l [Lag/hot 97901 Exercise 2. Use Stokes’ Theorem to calculate fCF dr Where F(a:,y,z)=_m1-l- 6"” j + 6" k and ' C' is the boundary of the portion of the plane 201+ y+ 2z— - 5 1n the tirst octant orientecl positively as viewed from above. ' . . 3- HM COLA/Q?" (Rb Qi‘ba'l’ajz /EI<J *(gx Pal: % (0 0)? +(o eyewtei’fk ,x 3/1, WWW W Ozxziawllléjég’ax 0-10.!leng r0903 wards—x £32 mama—em 09945 9.0/1- ea, L J l4 ’3' ..H.;,?rl‘xxfy l 0 4;\¢+7j+71_31_ 0 I”? 2 ' X i 111 Ml“ _ a S/R 7 ' "— e’ v _- ‘ , MATH 53 Discussion — Kaspar Exercise 3' Let F be a vector field 31 the upper half of the unit sphere (i e x2 + y2 + 22 =1 2 > 0) and S; the portion of the paraboloid z— — 1 m (at2 + yz) where z > 0,- both surfaces oriented upward. Use Stokes Theorem to show ffs curlF- dS= [sz curlF- dS ' flaw/111301? £1? -chwmg+,1w ’WW 473% _ _ WW5 Wwfifi‘i? f” 1111,3115th m 115. we-e’eflmefi -_-;.Exercise 4. Use the Divergence Theorem to calculate ffSF dS, Where F— = e” sinyi + em cosyj 4f— 1312'2 k and Sis the 'surface of the box 0 _<_ a: < 1,0 < y__ < 1,0 < z < 2 oriented outward. HWWF (2W3)k+(2wo3\3(152);— 60M) ~2W3 +33? :292 ...
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