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Unformatted text preview: MATH 32B PRACTICE MIDTERM October, 22nd, 2007 Problem 1. Consider the integral I = 2 0 f (x, y)dxdy, where f (x, y) = ex y . Divide the rectangle [2, 0] [0, 2] into 4 equal squares. Let L be the Riemann sum corresponding to this subdivision and sample points being left lower corners. Let R be the Riemann sum corresponding to the right lower corners. Which of the following inequalities are true: I < L I < R 0 2 2 2 Problem 2. Find the volume of the solid bounded by the surface z = 1 + ex sin y and the planes x = 1, y = 0, y = , z = 0. Problem 3. Use double integral to find the area enclosed by the curve r = 4 + 3 cos . Problem 4. Find the surface area of the surface z = xy that lies within the cylinder x2 + y 2 = 1 . Problem 5. Let D be a square lamina with vertices (0, 0), (0, 1), (1, 0), (1, 1) and density proportional to the distance to the yaxis. Find the moment of this lamina with respect to the axis with equation y = x.
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This note was uploaded on 04/06/2008 for the course MATH 32B taught by Professor Rogawski during the Spring '08 term at UCLA.
 Spring '08
 Rogawski
 Division

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