UCI
MATH 2E -
Quiz 7
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Math 2E 44275 Spring 2014 Quiz 7 6 05 14 Name Print ID Number Show all of your work Partial credit will be given 1 10 points Use the divergence theorem to calculate the ux of the vector eld F x3i 3yz2j 3y2z x2 k out of the sphere S with equation x2 y2 z2 4 Solution The divergence of F is given by By the divergence theorem ZZ F dS S divF 3x2 3y2 3z2 divF dV Z E Z 2 0 0 ZZZ ZZZ Z 2 E 0 3 25 5 12 25 3 5 3 x2 y2 z2 dV 2 2 sin d d d cos 0 2
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