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Solved: Remainder terms Find the remainder in the Taylor

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 48E Chapter 9.3

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 48E

Problem 48E

Remainder terms Find the remainder in the Taylor series centered at the point a for the following functions. Then show that  for all x in the interval of convergence.

f(x)= cos 2x, a = 0

Step-by-Step Solution:

Solution 48E

Step 1:

First we find the Taylor series of  f(x)=sin  a ,at a=0 as follows

f(x)=cos 2x   f(0)=1

f’(x)=-2 sin 2x   f’(0)=0

f’’(x)=-4cos 2x   f’’(0)=-4

f’’’(x)=8 sin 2x   f’’’(0)=0

f’’’’(x)=16 cos 2x   f’’’’(0)=16

Since the derivatives repeat in a cycle of four, we can write the Maclaurin series as follows:

 

=

=

Step 2 of 4

Chapter 9.3, Problem 48E is Solved
Step 3 of 4

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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Solved: Remainder terms Find the remainder in the Taylor