a. Explanation Given: The function f ( x ) = 1 + x 4 . Theorem used: Binomial series “For real number p ≠ 0 , the Taylor series for f ( x ) = ( 1 + x ) p centered at 0 is, ∑ k = 0 ∞ ( p k ) x k = ( p 0 ) + ( p 1 ) x + ( p 2 ) x 2 + ⋯ (1) Calculation: The first four nonzero terms of the binomial series centered at 0 is computed as follows, Substitute p = 1 4 in f ( x ) = ( 1 + x ) p , ( 1 + x ) 1 4 = ( 1 4 0 ) + ( 1 4 1 ) x + ( 1 4 2 ) x 2 + ( 1 4 < b. To determine To approximate: The value 1.12 4 by using part ( a ).

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 9.3, Problem 41E

To determine

To find: The first four nonzero terms of the binomial series centered at 0.

To determine

To approximate: The value 1.124 by using part (a).

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Chapter 9.3, Problem 40E

Chapter 9.3, Problem 42E

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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 first four nonzero terms of the binomial series centered at 0.

Solution Summary: Theorem: The first four nonzero terms of the binomial series centered at 0 is computed as follows.

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To find: The first four nonzero terms of the binomial series centered at 0.

To approximate: The value 1.124 by using part (a).

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Chapter 9 Solutions