126FinalSpring07

# 126FinalSpring07 - MATH 126 FINAL EXAM May 7 2007 Last Name...

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MATH 126 FINAL EXAM May 7, 2007 Last Name: First Name: Student ID Number: Signature: Circle your instructor’s name: Bene (10 am) Bene (11 am) Honda Lanski Mancera Mikulevicius INSTRUCTIONS Answer all the questions. You must show your work to obtain full credit. Points may be deducted if you do not justify your final answer. Please indicate clearly whenever you continue your work on the back of the page. Calculators are not allowed. The exam is worth a total of 200 points. Problem Value Score 1 10 2 40 3 15 4 20 5 15 6 10 7 10 8 20 9 30 10 10 11 20 Total 200 1

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1. (10 points) Find the limit if it exists: lim x 0 e x - 1 - x cos (2 x ) - cos (3 x ) 2. (40 points) Evaluate the following integrals. (a) Z x tan 2 ( x ) dx Continued on the next page. 2
Continued from the previous page. (b) Z 2 x 4 + x 2 dx (c) Z x 3 1 - x 2 dx 3

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3. (15 points) Evaluate the integral Z 1 0 ln x dx . 4. (20 points) Consider the region R bounded by y = x 2 - 6 and y = x . Set up, but do not evaluate , an integral for the volume of the solid obtained by rotating the region R (a) about the line y = 6.
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