Explanation Given: The series 1 + x : 1 + 1 2 x − 1 2 ⋅ 4 x 2 + 1 ⋅ 3 2 ⋅ 4 ⋅ 6 x 3 − ⋯ Result used: The binomial series for f ( x ) = ( 1 + x ) p centered at 0 is ( 1 + x ) p = ∑ k = 0 ∞ ( p k ) x k , for | x | < 1 . The Binomial coefficient c k = p ( p − 1 ) ⋯ ( p − k + 1 ) k ! Calculation: The binomial series for f ( x ) = ( 1 + x ) 1 2 Compute the fourth term coefficient of the Binomial series as follows, c 4 = 1 2 ( 1 2 − 1 ) ( 1 2 − 2 ) ( 1 2 − 3 ) 4 ! = 1 2 ( − 1 2 ) ( − 3 2 ) ( − 5 2 ) 2 ⋅ 3 ⋅ 4 = − 1 ⋅ 3 ⋅ 5 2 ⋅ 4 ⋅ 6 ⋅ 8 That is, c 4 = − 1 ⋅ 3 ⋅ 5 2 ⋅ 4 ⋅ 6 ⋅ 8

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

2nd Edition

ISBN: 9780321954329

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

Publisher: PEARSON

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Chapter 9.3, Problem 80E

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To find: The next two terms of the Taylor series.

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Chapter 9.3, Problem 79E

Chapter 9.3, Problem 81E

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Chapter 9 Solutions

Student Solutions Manual, Single Variable for Calculus: Early Transcendentals

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 next two terms of the Taylor series.

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Chapter 9 Solutions