Pre-Calc Homework Solutions 398

Pre-Calc Homework Solutions 398 - 398 Chapter 9 Review (b)...

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58. continued (c) f 1 2} 1 4 } 2 5 } 2 3 } , so one percent is approximately 0.0067. It takes 7 terms (up through degree 6). This can be found by trial and error. Also, for x 52} 1 4 } , the series is the alternating series n 5 0 1 2} 1 2 } 2 n . If you use the Alternating Series Estimation Theorem, it shows that 8 terms (up through degree 7) are sufficient since ) 2} 1 2 } ) 8 , 0.0067. It is also a geometric series, and you could use the remainder formula for a geometric series to determine the number of terms needed. (See Example 2 in Section 9.3.) 59. (a) lim n ) } a a n 1 n 1 } ) 5 lim n ? } ) x n ) n ! n n } 5 lim n 5 ) x ) lim n 1 } n 1 n 1 } 2 n 5 ) x ) e The series converges for ) x ) e , 1, or ) x ) , } 1 e } , so the radius of convergence is } 1 e } . (b) f 1 2} 1 3 } 2 < 2} 1 3 } ? } 1 1 } 1 1 2} 1 3 } 2 2 ? } 2 2 2 ! } 1 1 2} 1 3 } 2 3 ? } 3
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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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