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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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Given:
4х — 6
f(x) :
1- (2х — 3)3
a) Find the Taylor series representation for f about x=1.5 that is valid for all x e (1,2)
-Use the equation = E-o t", where t E
(-1,1) to find the Taylor series representatiom for(2x-3)=
4n=0
1-
1
about x = 1.5
- Then, use found Taylor series representation to find the series representation for f.
b) Use the result in "a)" to find the 4th degree Taylor polynomial of f about 1.5
c) Use the result in "b)" to approximate f(1.55).
Transcribed Image Text:Given: 4х — 6 f(x) : 1- (2х — 3)3 a) Find the Taylor series representation for f about x=1.5 that is valid for all x e (1,2) -Use the equation = E-o t", where t E (-1,1) to find the Taylor series representatiom for(2x-3)= 4n=0 1- 1 about x = 1.5 - Then, use found Taylor series representation to find the series representation for f. b) Use the result in "a)" to find the 4th degree Taylor polynomial of f about 1.5 c) Use the result in "b)" to approximate f(1.55).
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