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FinalReview

# FinalReview - Simca Bouma and Rob Rovai Math 126 1 Solve...

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Simca Bouma and Rob Rovai Math 126 Final Review Spring 2011 college.usc.edu/math126 www-scf.usc.edu/˜bouma 1. Solve the following limits. (a) lim x 0 (cos x ) 1 /x 2 (b) lim x 1 sin 2 ( πx ) ( x - 1) 2 2. Compute the integral or establish divergence. (a) Z π/ 2 arctan x x 2 d x (b) Z 1 2 + sin x 3 1 + x 2 + x 4 d x

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Math 126 Final Review Spring 2011 Page 2of ?? college.usc.edu/math126 3. Compute the integral. (a) Z 3 1 / 3 x x 2 + x d x (b) Z π/ 2 0 sin 2 x cos 2 x d x (c) Z x 3 - x 4 d x (d) Z x 3 e x 2 d x
Math 126 Final Review Spring 2011 Page 3of ?? college.usc.edu/math126 (e) Z 3 ( x - 1)( x 2 + x + 1) 4. Consider the region R bounded by the function y = x , the x -axis, and the line x = 1. (a) Set up but DO NOT EVALUATE an integral for the volume of the solid obtained by rotating R about x = 2. (b) Set up but DO NOT EVALUATE an integral for the volume of the solid obtained by rotating R about the line y = 1. 5. A leaky 10 kg bucket is lifted from the ground to a height of 20 m at a constant speed with a rope that

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FinalReview - Simca Bouma and Rob Rovai Math 126 1 Solve...

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