anskeyevenreview2

anskeyevenreview2 - MATH 1042 Fall 2010 Answer Key to Even...

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Unformatted text preview: MATH 1042 Fall 2010 Answer Key to Even and Modified Review Problems for Test 2 Section 7.4 √ 1√ 17 − 5 8. 4 Section 7.6 6. 1 16. 25 √ x2 − 5 x +C x2 − 3x + 11 ln |x + 3| + C 2 30. 2 ln |x − 1| + 1 ln |x2 + 1| − 3 tan−1 x + C 2 Section 7.7 24. Diverges Chapter 7 Review Problems π 86. 2 Section 10.1 38. 0 Section 10.2 n−1 n−1 = 1 = 0, therefore, lim (−1)n does not exist and the series diverges by 14. lim n→∞ n→∞ n n the Divergence Test. 24. S = 1 e−1 28. S = 4 30. S = 7 15 Section 10.3 1 1 1 converges (p = 2 > 1), and 18. The inequality 2 √ ≤ 2 is useful since the series n n2 n+ n n=1 if the terms of a positive series are smaller than the terms of a convergent series, the series also converges. ln n 1 < 2 ; the series converges by the Comparison Test n3 n n 1 n 36. √ > √ = √ ; the series diverges by the Comparison Test 3−1 3 n n n 30. 0 ≤ 56. lim 21/k = 1 = 0; the series diverges by the Divergence Test k→∞ ∞ Section 10.4 ∞ 6. Converges absolutely by Direct Comparison with n=1 1 n2 8. Diverges by the Divergence Test ∞ 22. Diverges by the Limit Comparison Test with n=1 1 n Section 10.5 2. Converges 6. Diverges 10. Converges 44. Converges by the Integral Test 38. Diverges by the Divergence Test 48. Diverges by the Divergence Test Chapter 10 Review Exercises 35 (modified). The series converges conditionally. Alternating Series Test gives convergence, 1 Limit Comparison Test with shows it does not converge absolutely. n ...
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anskeyevenreview2 - MATH 1042 Fall 2010 Answer Key to Even...

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