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234-slemrod-05fa02 - Math 234 M Slemrod Exam 2 Thursday...

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Unformatted text preview: Math 234 ' M. Slemrod Exam 2 Thursday, November 17, 2005 NAME: TA’s NAME: Calculators okay! Show your work! Problem Math 234 Page 1 /S / sin(y2)dA where Sis the region as g y 31, 0 S x g 1. 1. Evaluate the integral (Hint: The region is both :r—simple and y-simple but one of these two is a better choice.) (30 pts) Math 234 Page 2 2. Find the maximum volume of the closed rectangular box with faces parallel to the coordinate planes inscribed in the ellipsoid + 2 2 z —:3. 33+ 9 E 4 (30 pts) Math 234 Page 3 3. Find the area of the surface G' cut from the hemisphere x2+y2+z22R2, 220 and the planes 2 = A,‘ z = B, R > A > B. , t. ‘» (Hint: Polar cordinates may proi/e helpful in evaluating integrals.) (40 pts) ...
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