a. Explanation Given: The function f ( x ) = 10 x , a = 2 . Result used: The Taylor series centered at a is, f ( x ) = f ( a ) + f ′ ( a ) ( x − a ) + f ″ ( a ) ( x − a ) 2 2 ! + f ‴ ( a ) ( x − a ) 3 3 ! + ⋯ = ∑ k = 0 ∞ f ( k ) ( a ) k ! ( x − a ) k Calculation: Obtain the first four nonzero terms of the Taylor series f ( x ) = 10 x centered a = 2 . The value of f ( x ) = 10 x and its derivatives at x = 2 are computed in the below table, k f k ( x ) f k ( 2 ) 0 f ( x ) = 10 x f ( 2 ) = 100 1 f ′ ( x ) = ln ( 10 ) ⋅ 10 x f ′ ( 2 ) = ln ( 10 ) ⋅ 100 2 f ″ ( x ) = ln 2 ( 10 ) ⋅ 10 x f ″ ( 2 ) = ln 2 ( 10 ) ⋅ 100 3 f ‴ ( x ) = ln 3 ( 10 ) ⋅ 10 x f ‴ ( 2 ) = ln 3 ( 10 ) ⋅ 100 The Taylor series centered at a = 2 is computed as follows, f ( x ) = f ( 2 ) + f ′ ( 2 ) b. To determine To write: The power series using summation notation.

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 28E

To determine

To find: The first four nonzero terms of the Taylor series for given function centered at a.

To determine

To write: The power series using summation notation.

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Chapter 9.3, Problem 27E

Chapter 9.3, Problem 29E

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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 first four nonzero terms of the Taylor series for given function centered at a.

Solution Summary: The author explains how to obtain the first four nonzero terms of the Taylor series for given function centered at a.

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To find: The first four nonzero terms of the Taylor series for given function centered at a.

To write: The power series using summation notation.

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Chapter 9 Solutions