4х — 6 2. Let f(x) 1- (2г — 3)3 (a) Find the Taylor series representation for f about x = 1.5 that is valid for all x E (1, 2). +o0 1 Hint: Use the equation > t", where t € (-1,1), to find the Taylor series representation for 1- t n=0 1 about x = 1.5. Then, use this series to find the desired series representation for f. 1- (2х — 3)3 (b) Use the result in (2a) to find the 4th degree Taylor polynomial of f about 1.5. (c) Use the result in (2b) to approximate f(1.55). Express your answer in decimal form.
4х — 6 2. Let f(x) 1- (2г — 3)3 (a) Find the Taylor series representation for f about x = 1.5 that is valid for all x E (1, 2). +o0 1 Hint: Use the equation > t", where t € (-1,1), to find the Taylor series representation for 1- t n=0 1 about x = 1.5. Then, use this series to find the desired series representation for f. 1- (2х — 3)3 (b) Use the result in (2a) to find the 4th degree Taylor polynomial of f about 1.5. (c) Use the result in (2b) to approximate f(1.55). 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:4х — 6
2. Let f(x)
1- (2г — 3)3
(a) Find the Taylor series representation for f about x = 1.5 that is valid for all x E (1, 2).
+00
1
Hint: Use the equation
> t", where t € (-1,1), to find the Taylor series representation for
1- t
n=0
1
about x = 1.5. Then, use this series to find the desired series representation for f.
1— (2х — 3)3
(b) Use the result in (2a) to find the 4th degree Taylor polynomial of f about 1.5.
(c) Use the result in (2b) to approximate f(1.55). Express your answer in decimal form.
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