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4x-10 Let f(x)= 1-(2x-5)** a. Find the Taylor series representation for f about x = 2.5 that is valid for all x € (2,3). Hint: Use the equation = [t", where t € (-1,1), to find the Taylor series representation for 1-(2x-5)4 about x = 2.5. Then, use this series to find the desired series representation for f. b. Use the result in item 2(a) to find the 5th degree Taylor polynomial of f about 2.5. c. Use the result in item 2(b) to approximate f(2.55). Express your answer in decimal form.

4x-10 Let f(x)= 1-(2x-5)** a. Find the Taylor series representation for f about x = 2.5 that is valid for all x € (2,3). Hint: Use the equation = [t", where t € (-1,1), to find the Taylor series representation for 1-(2x-5)4 about x = 2.5. Then, use this series to find the desired series representation for f. b. Use the result in item 2(a) to find the 5th degree Taylor polynomial of f about 2.5. c. Use the result in item 2(b) to approximate f(2.55). Express your answer in decimal form.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4x - 10 Let f(x)=1-(2x-5)4¹ a. Find the Taylor series representation for f about x = 2.5 that is valid for all x € (2,3). Hint: Use the equation t", where t € (-1,1), to find the Taylor series representation for x=0 1 about x = 2.5. Then, use this series to find the desired series representation for f. 1-(2x-5)* b. Use the result in item 2(a) to find the 5th degree Taylor polynomial of f about 2.5. c. Use the result in item 2(b) to approximate f(2.55). Express your answer in decimal form. +00
Transcribed Image Text:4x - 10 Let f(x)=1-(2x-5)4¹ a. Find the Taylor series representation for f about x = 2.5 that is valid for all x € (2,3). Hint: Use the equation t", where t € (-1,1), to find the Taylor series representation for x=0 1 about x = 2.5. Then, use this series to find the desired series representation for f. 1-(2x-5)* b. Use the result in item 2(a) to find the 5th degree Taylor polynomial of f about 2.5. c. Use the result in item 2(b) to approximate f(2.55). Express your answer in decimal form. +00
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