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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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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.
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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