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Answer: Convergence Write the remainder term Rn (x) for

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

Solution for problem 40RE Chapter 9

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 40RE

Write the remainder term \(R_n(x)\) for the Taylor series for the following functions centered at the given point a. Then show that \(\lim _{n \rightarrow \infty} R_{n}(x)=0\) for all x in the given interval.

\(f(x)=\sqrt{1+x},\ \ a=0,\ \ -\frac{1}{2}\ \leq\ x\ \leq\ \frac{1}{2}\)

Step-by-Step Solution:

Solution 40RE

Step 1:

First we find the Taylor series of   ,at a=0 as follows

 

Thus the Taylor series of  with center 0 is as follows

Step 2 of 4

Chapter 9, Problem 40RE is Solved
Step 3 of 4

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

Since the solution to 40RE from 9 chapter was answered, more than 352 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. This full solution covers the following key subjects: given, Remainder, functions, Centered, interval. This expansive textbook survival guide covers 112 chapters, and 7700 solutions. The full step-by-step solution to problem: 40RE from chapter: 9 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “?Write the remainder term \(R_n(x)\) for the Taylor series for the following functions centered at the given point a. Then show that \(\lim _{n \rightarrow \infty} R_{n}(x)=0\) for all x in the given interval.\(f(x)=\sqrt{1+x},\ \ a=0,\ \ -\frac{1}{2}\ \leq\ x\ \leq\ \frac{1}{2}\)” is broken down into a number of easy to follow steps, and 42 words. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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Answer: Convergence Write the remainder term Rn (x) for