MATH 251H Final Exam Version B Solutions

# B c d e yz xz xy correct choice 1 12 2

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Unformatted text preview: density as fast as possible? 2, 2, 1 2, 2, 1 333 2, 2, 1 2, 2, 1 333 2, 2, 1 333 a. b. c. d. e.    yz, xz, xy Correct Choice   1, 1,2   2, 2, 1 441  3 He should travel in the direction      2, 2, 1 v ÞÞ e x 8. Compute a.  e 2 c. d. e. ÞÞ e x 2 y2 dA over the quarter circle x 2  y 2 2, 2, 1 . 333 9 in the first quadrant. 9 2  e9 1 2 e 9 4  1 e9 4 1 e9 b. y2 or the unit direction v  dA  Correct Choice /2 Þ 0 Þ 0 e r r dr d  Þ0 Þx 8 9. Compute 2 1/3 3 2  2 r2 3 2 e 0 1 4 e 9 cos y 2 dy dx HINT: Reverse the order of integration. a. 1 sin 4 1 4 4 1 sin 64 1 b. 4 4 1 sin 64 c. 4 1 d. 1 sin 16 4 4 1 sin 16 e. Correct Choice 4 Plot the region. Reverse the order. Compute new limits: y  x 1/3 Þ0 Þx 8 2 cos y 2 dy dx  1/3  Þ 0 y 3 cos y 4 2 y3 Þ0 Þ0 2 dy  Í cos y 4 dx dy  sin y 4 4 y x  y3 2 yo Þ 0 cos y 4 2  1 sin 16 4 x y3 x0 dy 2 1 0 0 2 4 6 8 x 3 10. ÞÞÞ z dV Compute over the solid sphere x 2  y 2  z 1 2 1 given in spherical coordinates by   2 cos . HINT: The whole sphere has z 0. What does this say about ? a. 2 3 4 b. Correct Choice 3 c. 4 6  d. 3 e.  12 z   cos  dV   2 sin  d d d 2 cos  4 /2 2 2 cos  /2 cos  sin  d ÞÞÞ z dV  Þ 0 Þ 0 Þ 0  cos   2 sin  d d d  2 Þ 0  40  2 Þ 11. Compute from...
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## This note was uploaded on 02/06/2014 for the course MATH 251H taught by Professor Philipb.yasskin during the Spring '11 term at Texas A&M.

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