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APPM1360Fall07Final

# APPM1360Fall07Final - APPM 1360 FINAL EXAM FALL 2007 On the...

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APPM 1360 FINAL EXAM FALL 2007 On the front of your bluebook, please write: a grading key, your name, student ID, and section and instructor (Dougherty, section 10, or Li, section 30 with lecture at 1 pm or section 20 with lecture at 2 pm). This exam is worth 200 points and has 7 questions. Show all work! Answers with no justification will receive no points. Please begin each problem on a new page. 1. (40 points) Evaluate the following integrals and limits. If the integral or limit diverges, explain why. ( a ) Z π 2 0 cos( x ) q 1 + sin( x ) dx ( b ) Z 2 0 1 ( t - 1) 5 dt ( c ) Z 1 x 2 - 3 x dx ( d ) lim x 0 + cos( x ) - 1 + x 2 x 2 ( e ) lim n →∞ (1 - x n ) n 2. (25 points) Find the x -coordinate of the center of mass of a thin plate of constant density covering the region enclosed by the curve y = ln x and the x -axis for 1 x e . 3. (25 points) For this problem, consider the curve y = x 3 on the interval 0 x 2. Set up, but do not evaluate, the integrals to find the requested quantities.

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APPM1360Fall07Final - APPM 1360 FINAL EXAM FALL 2007 On the...

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