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Remainder terms Find the remainder in the Taylor series

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

Solution for problem 47E 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 47E

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) = sin a, a = 0

Step-by-Step Solution:

Solution 47E

Step 1:

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

f(x)=sin x   f(0)=0

f’(x)=cos x   f’(0)=1

f’’(x)=-sin x   f’’(0)=0

f’’’(x)=-cos x   f’’’(0)=-1

f’’’’(x)=sin x   f’’’’(0)=0

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

 

=

=

Step 2:

With , we have

Since  is  , we know that  for all .

For  ,

Step 3 of 4

Chapter 9.3, Problem 47E is Solved
Step 4 of 4

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

The full step-by-step solution to problem: 47E from chapter: 9.3 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: Remainder, Centered, Find, functions, interval. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 47E from 9.3 chapter was answered, more than 269 students have viewed the full step-by-step answer. The answer to “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) = sin a, a = 0” is broken down into a number of easy to follow steps, and 35 words.

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