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fin - Calculus II V1102 Section 007 Fall 2007 Final Exam...

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Calculus II V1102 Section 007, Fall 2007 Final Exam Thomas D. Peters Name: December 18, 2007 Do all problems, in any order. Show your work. An answer alone may not receive full credit. No notes, texts, or calculators may be used on this exam. Problem Possible Points Points Earned 1 8 2 13 3 9 4 5 5 4 6 6 7 5 8 5 9 5 10 9 11 6 TOTAL 75 1
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1. (a)(4 pts) Compute e 2 x e 2 x + 1 dx (b)(4 pts) Compute e x e 2 x + 1 dx 2
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2. In this problem we find the exact value of S = n =0 ( - 1) n 3 n + 1 (a)(2 pts) Explain why S converges. (b)(3 pts) Show that S = 1 0 dt 1 + t 3 by expanding the integrand as a series and integrating term by term. (c)(3 pts) Use partial fractions to decompose 1 t 3 + 1 (d)(5 pts) Use your answer from (c) to compute 1 0 dt 1 + t 3 . 3
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3. True or false. You MUST explain your answer (a)(3 pts) If { a n } and { b n } are divergent sequences then { a n b n } is also a divergent sequence. (b)(3 pts) If a n converges and a n > 0 for all n then a n is eventually decreasing.
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