Pre-Calc Homework Solutions 387

Pre-Calc Homework Solutions 387 - Section 9.5 Quick Review...

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Quick Review 9.5 1. Converges, since it is of the form E 1 } x 1 p } dx with p . 1 2. Diverges, limit comparison test with integral of } 1 x } 3. Diverges, comparison test with integral of } 1 x } 4. Converges, comparison test with integral of } x 2 2 } 5. Diverges, limit comparison test with integral of } ˇ 1 x w } 6. Yes, for N 5 0 7. Yes, for N 5 2 ˇ 2 w 8. No, neither positive nor decreasing for x . ˇ 3 w 9. No, oscillates 10. No, not positive for x $ 1 Section 9.5 Exercises 1. Diverges by the Integral Test, since E 1 } x 1 5 1 } dx diverges. 2. Diverges because n 5 1 } ˇ 3 n w } 5 3 n 5 1 } n 1 1/2 } , which diverges by the p -series Test. 3. Diverges by the Direct Comparison Test, since } ln n n } . } 1 n } for n $ 2 and n 5 2 } 1 n } diverges. 4. Diverges by the Integral Test, since E 1 } 2 x 1 2 1 } dx diverges. 5. Diverges, since it is a geometric series with r 5 } ln 1 2 } < 1.44. 6. Converges, since it is a geometric series with r 5 } ln 1 3 } < 0.91. 7. Diverges by the n th-Term Test, since lim n n sin } 1 n } 5 1.
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.

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