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e3 - EXAM Exam 2 Takehome Exam Math 2350-02&04 Spring 2008...

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EXAM Exam 2 Takehome Exam Math 2350-02&04, Spring 2008 April 23, 2008 Corrected Version April 28, 2008 This is a Takehome Exam. You may discuss the problems with others, but write up your own solutions. If not otherwise instructed, you can use a calculator to do the integrals, but state exactly what you used the calculator to compute. You must show enough work to justify your answers. Unless otherwise instructed, give exact answers, not approximations (e.g., 2, not 1 . 414). This exam has 8 problems. There are 340 points total . Good luck!
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Problem 1 . Let R be the region in the upper half-plane bounded by the circles 40 pts. x 2 + y 2 = 1 and x 2 + y 2 = 9. Find ¯ y , the y -coordinate of the centeroid of R . Problem 2 . Let R be the region in three dimensional which lies in the first 60 pts. octant and is bounded by xz -coordinate plane, the yz -coordinate plane, above by the paraboloid z = 2 - x 2 - y 2 and below by the plane z = 1. A. Set up an iterated integral for finding the volume of R , where the first integration is with respect to y . Evaluate the integral by hand computation.
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