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Unformatted text preview: 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! 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....
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