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APPM1360Fall07Test2

APPM1360Fall07Test2 - APPM 1360 EXAM#2 FALL 2007 On the...

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APPM 1360 EXAM #2 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 100 points and has 5 questions. A list of formulas is given on the back of this exam. Show all work! Answers with no justification will receive no points. 1. (30 points) Evaluate the following integrals. If an integral is improper, determine whether it converges or diverges. If it converges, evaluate it. If it diverges, justify your answer. ( a ) e 1 x ln( x ) dx ( b ) 1 / 2 0 6 1 - 4 x 2 dx ( c ) 1 - 1 1 t 3 dt 2. (20 points) Determine whether the following sequences converge or diverge. If the sequence converges, find its limit. ( a ) a n = 1 + ( - 1) n ( b ) b n = 1 n 2 + n - n 2 + 1 for n 2 ( c ) c n = n ln 1 + 2 n 3. (15 points) Consider the sequence a n = 3 n ( n + 1) and the series n =1 a n . (a) Does the sequence { a n } converge? If so, what is its limit?
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