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Unformatted text preview: f ( x, y, z ) = x 2 y 2 z 2 on the sphere x 2 + y 2 + z 2 = 1 using Lagrange multipliers. ANSWER: 4 4. (10 points) Sketch the region of integration for the integral Z π Z π x sin y y d y d x. Then reverse the order of integration and do the integral. (Hint: You will probably not be able to do the integral without changing the order of integration.) ANSWER: 5 5. (10 points) Find the volume of the solid shown in the ﬁgure below. It is bounded on the bottom by the xy plane, on the sides by the sphere centered at the origin of radius 2 and on the top by a cone which makes an angle of π/ 3 radians with the zaxis. (Hint: Integrate in spherical coordinates.) x y z π/ 3 6...
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 Spring '08
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 Math, Calculus, Derivative

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