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mid1w - Math 126 C Spring 2007 Mid-Term Exam Number One...

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Math 126 C - Spring 2007 Mid-Term Exam Number One April 19, 2007 Name: Section: 1 10 2 10 3 10 4 10 5 10 Total 50 Complete all questions. You may use a scientific, non-graphing calculator during this examination. Other elec- tronic devices are not allowed, and should be turned off for the duration of the exam. If you use a trial-and-error or guess-and-check method, or read a numerical solution from a graph on your calculator, when an algebraic method is available, you will not receive full credit. You may use one hand-written 8.5 by 11 inch page of notes. Show all work for full credit. You have 50 minutes to complete the exam. .
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1. Let f ( x ) = e x sin x . (a) Find the second-order Taylor polynomial T 2 ( x ) for f ( x ) based at b = 0 . (b) Give a bound on the error | f ( x ) - T 2 ( x ) | for x in the interval - 0 . 1 x 0 . 1 .
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2. Find the first four non-zero terms of the Taylor series for
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