32B(W08)_PracticeMidterm1

32B(W08)_PracticeMidterm1 - cos(3 x 2 dxdy 5 4(15 points A...

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MATH 32B - Lecture 4 - Winter 2008 Practice Midterm 1 - January 30, 2008 NAME: STUDENT ID #: This is a closed-book and closed-note examination. Calculators are not allowed. Please show all your work. Use only the paper provided. You may write on the back if you need more space, but clearly indicate this on the front. There are 6 problems for a total of 100 points. 1
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2 1.(15 points) Evaluate Z Z Z E x 2 e y dV where E is bounded by the parabolic cylinder z = 1 - y 2 and the planes z = 0, x = 1 and x = - 1.
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3 2.(20 points) Find the area of the part of the sphere x 2 + y 2 + z 2 = a 2 that lies within the cylinder x 2 + y 2 = ax and above the xy -plane.
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4 3.(15 points) Calculate the iterated integral Z 1 0 Z 1 y
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Unformatted text preview: cos(3 x 2 ) dxdy 5 4.(15 points) A lamina occupies the region inside the circle x 2 + y 2 = 2 y but outside the circle x 2 + y 2 = 1. Find the center of mass if the density at any point ( x,y ) is ρ ( x,y ) = 3 √ x 2 + y 2 6 5.(20 points) Use the transformation x = u v ,y = v to evaluate Z Z R xydA, where R is the region in the first quadrant bounded by the lines y = x and y = 3 x and the hyperbolas xy = 1 and xy = 3. 7 6.(15 points) Find the volume of the solid that lies within the sphere x 2 + y 2 + z 2 = 4, above the xy-plane and below the cone z = p 3 x 2 + 3 y 2 ....
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This note was uploaded on 05/01/2008 for the course MATH 32B taught by Professor Rogawski during the Winter '08 term at UCLA.

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32B(W08)_PracticeMidterm1 - cos(3 x 2 dxdy 5 4(15 points A...

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