100hw5 - z = x 2 + y 2 that is inside the cylinder x 2 + y...

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Math 100 Homework 5 fall 2010 due 12/11 1. (14.2, 42) Evaluate the volume of the solid enclosed by y 2 = x , z = 0, and x + z = 1. 2. (14.2, 50) Express Z e 1 Z ln x 0 f ( x, y ) dydx as an equivalent integral with the order of integration reversed. 3. (14.3, 28) Evaluate Z 2 - 2 Z 4 - y 2 - 4 - y 2 e - ( x 2 + y 2 ) dxdy by converting to polar coordinates. 4. (review exercise 14, 18) Convert to polar coordinates and evaluate Z 2 0 Z 4 - x 2 x 4 xydydx. 5. (14.4, 8) Evaluate the surface area of the portion of the paraboloid 2
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Unformatted text preview: z = x 2 + y 2 that is inside the cylinder x 2 + y 2 = 3. 6. (14.4, 42) Find the equation of the tangent plane to the parametric surface r ( u, v ) = ( uv, u-v, u + v ) at r (1 , 2). 7. (review exercise 14, 4b) Write down a parametrization of the right circular cylinder of radius a and height h that is centered on the z-axis, has its base in the xy-plane, and extends in the positive z-direction. 1...
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