a. Explanation Given: The given function f ( x ) = 1 ( 1 − x ) 2 and ∑ k = 1 ∞ k x k − 1 for − 1 < x < 1 . Calculation: Obtain the first n terms of the series S n ( x ) . Substitute n = 5 in S n ( x ) as follows, S 5 ( x ) = ∑ n = 1 5 n x n − 1 = 1 x 1 − 1 + 2 x 2 − 1 + 3 x 3 − 1 + 4 x 4 − 1 + 5 x 5 − 1 = 1 + 2 x + 3 x 2 + 4 x 3 + 5 x 4 That is, S 5 ( x ) = 1 + 2 x + 3 x 2 + 4 x 3 + 5 x 4 . Use the online graphing calculator to draw the function f ( x ) and S 5 ( x ) . From the Figure 1, it is observed that the functions f ( x ) and S 5 ( x ) increasing rapidly at x = 0.09 b. To determine To explain: The value of n is needed to guarantee that | f ( x ) − S n ( x ) | < 0.01 at all of the sample points.

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 9.2, Problem 77E

To determine

To sketch: The graph of f(x) and Sn(x) with n=5 and n=10.

To determine

To explain: The value of n is needed to guarantee that |f(x)−Sn(x)|<0.01 at all of the sample points.

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Chapter 9.2, Problem 76E

Chapter 9.3, Problem 1E

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Chapter 9 Solutions

Calculus: Early Transcendentals (2nd Edition)

Ch. 9.1 - Suppose you use a second-order Taylor polynomial...Ch. 9.1 - Does the accuracy of an approximation given by a...Ch. 9.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 9.1 - Prob. 4E Ch. 9.1 - How is the remainder Rn(x) in a Taylor polynomial...Ch. 9.1 - Explain how to estimate the remainder in an...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...

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The graph of f ( x ) and S n ( x ) with n = 5 and n=10 .

Solution Summary: The author explains how to sketch the graph of f(x) and

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To sketch: The graph of f(x) and Sn(x) with n=5 and n=10.

To explain: The value of n is needed to guarantee that |f(x)−Sn(x)|<0.01 at all of the sample points.

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Chapter 9 Solutions