Pre-Calc Homework Solutions 391

Pre-Calc Homework Solutions 391 - Section 9.5 391 (b) S n 1...

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(b) S 5 n 5 1 } 3 n 2 n 1 1 } ? } 3 n } 5 n 5 1 } 3 n 2 3 1 1 } . This series converges by the Direct Comparison Test, since } 3 n 2 3 1 1 } , } n 1 2 } and n 5 1 } n 1 2 } is convergent as a p -series with p 5 2. 50. (a) From the list of Maclaurin series in Section 9.2, ln (1 1 x ) 5 x 2 } x 2 2 } 1 } x 3 3 } 2 1 ( 2 1) n 1 1 } x n n } 1 . (b) 2 1 , x # 1 (c) To estimate ln } 3 2 } , we would let x 5 } 1 2 } The truncation error is less than the magnitude of the sixth nonzero term, or ) 2} x 6 6 } ) 5 } 2 6 1 ? 6 } 5 } 3 1 84 } , 0.002605 Thus, a bound for the (absolute) truncation error is 0.002605. (d) n 5 1 } ( 2 1) 2 n n 1 1 x 2 n }5} 1 2 } n 5 1 } ( 2 1) n 1 n 1 ( x 2 ) n }5} 1 2 } ln (1 1 x 2 ) 51. lim k ) } a a k 1 k 1 } ) 5 lim k } l 2 n k 1 ( k 1 ) x 1 ) k 1 3 1 ) } ? } ln 2 ( k k ) x 1 ) k 2) }5 2 ) x ) The series converges absolutely for ) x ) , } 1 2 } , or 2} 1 2 } , x , } 1 2 } . Check
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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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