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homework13

# homework13 - Homework 13 — due 12/1 or 12/2 2 2[10...

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Math 1120 Homework13 Due 12/1 or 12/2,2011 Name: GRADES Book questions / 14 Presentation questions / 30 Print out these pages. Answer the “presentation questions” in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these prob- lems. Writeyouranswerstothe“bookquestions”onseparate paper and staple to these pages. They will be assessed only for completeness. Always write neatly and legibly. Book questions — 10 . 7 : 12 , 20 , 36 , 42 10 . 8 : 8 , 16 , 22 , 26 10 . 9 : 6 , 14 , 24 10 . 10 : 2 , 10 , 52 Presentation questions 1. [10points] Use the geometric series summationdisplay n =0 x n to find the sum of the series summationdisplay n =0 n ( n - 1) x n - 2 for | x | < 1. Fully justify your answer using results from the textbook or from class. CONTINUE TO THE NEXT PAGE.

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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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homework13 - Homework 13 — due 12/1 or 12/2 2 2[10...

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