Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

3rd Edition

ISBN: 9780134995991

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Textbook Question

Chapter 11.4, Problem 27E

Power series for derivatives

a. Differentiate the Taylor series about 0 for the following functions.
b. Identify the function represented by the differentiated series.
c. Give the interval of convergence of the power series for the derivative.

27. f(x) = ln (1 + x)

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Chapter 11.4, Problem 26E

Chapter 11.4, Problem 28E

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Chapter 11 Solutions

Calculus: Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

Ch. 11.1 - Verify that p3 satisfies p3(k)(a)=f(k)(a), for k =...Ch. 11.1 - Verify the following properties for f(x) = sin x...Ch. 11.1 - Why do the Taylor polynomials for sin x centered...Ch. 11.1 - Write out the next two Taylor polynomials p4 and...Ch. 11.1 - At what point would you center the Taylor...Ch. 11.1 - In Example 7, find an approximate upper bound for...Ch. 11.1 - Suppose you use a second-order Taylor polynomial...Ch. 11.1 - Does the accuracy of an approximation given by a...Ch. 11.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 11.1 - Suppose f(0) = 1, f(0) = 2, and f(0) = 1. Find the...

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Power series for derivatives a. Differentiate the Taylor series about 0 for the following functions. b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. 27. f ( x ) = ln (1 + x )

Solution Summary: The author explains that the derivative of the Taylor series is f(1+x)=mathrmln

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