Exam 3 Solutions Sp10

Exam 3 Solutions Sp10 - Math 237 Calculus II Exam 3 Fall...

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Math 237. Calculus II Exam 3 Fall, 2011 Name: SOLUTIONS _ Points : All questions are worth ten points except #6 and #9, which are worth 13, and #13, which is worth 14. Part I: Integrals. Find the following definite and indefinite integrals. If any integral is improper, decide whether it converges and, if so, then evaluate it. I'll find the indefinite integral using parts: So This is an improper integral. The indefinite integral can be found using substitution: . So the (proper) definite integral is And so the improper integral is equal to the limit For this one you make a trigonometric substitution. This is an improper integral since it goes off to –∞ as x approaches the upper limit of integration. Find the indefinite integral using substitution: ; . So the (proper) definite integral is Since , then the improper integral diverges.
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Part II: Sequences and Series. For each of the following, if the specified test is inconclusive, say so. 5. Use the n th -term test to determine whether the following series converge. (a) Since the limit of the n th term, , is not equal to zero, then this series diverges.
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