Exam 2 - E is the region in space bounded above by the...

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MATH 253.504–506 An unsupported answer Exam 2, version A is a wrong answer! 10/27/99 Notice that the only problems in which you are asked to evaluate an inte- gral are #1 and #7. 1. (15 pts.) Find y of the center of mass of the region 1 x 2 + y 2 9, y 0, if the density is constant. 2. (15 pts.) Use Lagrange multipliers to determine the maximum and minimum values of x +4 y on the ellipse x 2 +2 y 2 =1 ,andg iv ethe points where these occur. 3. (10 pts.) Convert Z 4 0 Z x 0 p x 2 + y 2 dy dx to an integral in polar coor- dinates, but don’t evaluate it. 4. (15 pts.) Reverse the order of integration to write Z 3 0 Z x +1 ( x - 1) 2 f ( x, y ) dy dx as the sum of 1 or more integrals in the order
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Unformatted text preview: E is the region in space bounded above by the sphere ( x-2) 2 + ( y + 1) 2 + z 2 = 25 and below by the plane z = 3. Set up, but do not evaluate Z ZZ E xz dV , in the order dz dy dx . 6. (15 pts.) Determine the maximum and minimum of f ( x, y ) = xy + 3 x on the closed region bounded above by y = 9-x 2 and below by the x axis, and give the points where they occur. 7. (15 pts.) Find the area of the part of the surface z = x + y 2 which lies above the triangle in the x , y plane with vertices (0 , 0), (0 , 2), and (2 , 2). (Hint: if you run into a hard integral, youve missed something.)...
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This note was uploaded on 03/26/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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