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Unformatted text preview: Homework 13 due 12/1 or 12/2 2 2. [10 points] (10.8: 39) Let f ( x ) have derivatives through order n at x = a . Show that the asscoiated Taylor polynomial of order n and its Frst n derivatives have the same values that f ( x ) and its Frst n derivatives have at x = a . CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 13 due 12/1 or 12/2 3 3. (10.9: 41, 42) (a) [5 points] The approximation e x = 1+ x +( x 2 / 2) is used when x is small. Use the Remainder Estimation Theorem (page 609) to estimate the error when | x | < . 1. (b) [5 points] When x < 0, the series for e x is an alternating series. Use the Alter-nating Series Estimation Theorem (page 588) to estimate the error that results from replacing e x by 1 + x + ( x 2 / 2) when-. 1 < x < 0. THIS IS THE LAST PAGE....
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