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

## Problem 39RE Chapter 9

Calculus: Early Transcendentals | 1st Edition

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Problem 39RE

Convergence Write the remainder term Rn (x) for the Taylor series for the following functions centered at the given point a Then show that  for all x in the given interval.

f(x) = ln(l + x), a = 0, -

Step-by-Step Solution:

Solution 39RE

Step 1 of  2:

In this problem we need to find the remainder term in the taylor  series expansion  of f(x) = ln(1 +x) at center a = 0 , and we have to prove that  = 0.

Thus the Taylor series of  with center 0 is as follows;

Given : f(x) = , then  f(0) =  = 0 , since

= = , then   =  = 1

= )= , then   =  = -1

= = , then   =  = 2

…………………….  ……………(2)

Therefore , the Taylor series of  with center 0 is as follows;

…….

ln(1+x) =  x - + -...........

=

Step 2 of 2

##### ISBN: 9780321570567

Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 39RE from chapter: 9 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. Since the solution to 39RE from 9 chapter was answered, more than 253 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 85 chapters, and 5218 solutions. The answer to “Convergence Write the remainder term Rn (x) for the Taylor series for the following functions centered at the given point a Then show that for all x in the given interval.f(x) = ln(l + x), a = 0, -” is broken down into a number of easy to follow steps, and 39 words.

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

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