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Unformatted text preview: f ( x, y ) = x 3 + y 33 x 2 + 3 y 28. 6. (10 points) Use Lagrange multipliers to fnd the maximum and minimum values oF the Function f ( x, y ) = 1 x1 y subject to the constraint 1 x 2 + 1 y 2 = 1. 7. Consider the integral Z Z D f ( x, y ) dA = Z 2 Z 3(1x 2 )3 q 1x 2 2 2 f ( x, y ) dy dx . (a) (8 points) Sketch the region of integration. (b) (8 points) Switch the order of integration in the above integral. (c) (8 points) Compute the integral Z Z D f ( x, y ) dA for the case f ( x, y ) = xy . 8. (10 points) Transform to polar coordinates and then evaluate the integral I = Z 11 Z √ 1x 2 ³ x 2 + y 2 ´ 3 / 2 dy dx. 9. (10 points) Find the volume of a parallelepiped whose base is a rectangle in the z = 0 plane given by 0 6 y 6 2 and 0 6 x 6 1, while the top side lies in the plane x + y + z = 3. x 3 y 3 3 z...
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 Spring '08
 Helton
 Math, Calculus, Laplace, dy dx

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