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 n=0 1 1-(2x-5) ¡ 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 off 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 n=0 1 1-(2x-5) ¡ 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 off 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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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.
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