TeamHw3 - subdivisions possible in each approximation 3...

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Math 116 Winter 2012 Team Homework 3 Problem 1 : Let n be a positive integer. Find a formula for I ( n ), where I ( n ) = 1 π Z π - π x 2 cos( nx ) dx. Problem 2 : Section 7.2 # 62. Problem 3 : The values of the function f ( x ) are given below x 0 0.5 1.0 1.5 2.0 2.5 3.0 f ( x ) 2 1.3 0.9 0.6 0.7 1.1 1.9 1. Find a formula for the volume V of the solid whose base is the region bounded by y = f ( x ), the x -axis, and the line x = 3 and its cross-sections perpendicular to the x -axis are semicircles. 2. Estimate V using the midpoint and the trapezoid rule. Use the largest amount of
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Unformatted text preview: subdivisions possible in each approximation. 3. Assume f ( x ) is continuous with no points of inflection on 0 ≤ x ≤ 3. (a) Are any of your approximations in the previous question guaranteed to give an underestimate of V ? (b) Which of your approximations do you expect to be more accurate? Problem 4 : Section 8.2 #50. 1...
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This note was uploaded on 02/08/2012 for the course MATH 116 taught by Professor Staff during the Winter '08 term at University of Michigan-Dearborn.

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