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Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 9 - Problem 40re
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 9 - Problem 40re

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

ISBN: 9780321570567 2

## Solution for problem 40RE Chapter 9

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

Step 3 of 4

##### 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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