Explanation Formula used: The Taylor series expansion for e x is e x = 1 + x + 1 2 ! x 2 + 1 3 ! x 3 + ⋯ + 1 n ! x n + ⋯ ( − ∞ < x < ∞ ) . Calculation: The function is given by f ( x ) = 1 2 ( e x + e − x ) . By using the above mentioned formula, find the Taylor series of the function f ( x ) = 1 2 ( e x + e − x ) at x = 0 as follows. f ( x ) = 1 2 ( e x + e − x ) = 1 2 ( 1 + x + 1 2 ! x 2 + 1 3 ! x 3 + ⋯ + 1 n ! x n + ⋯ + 1 + ( − x ) + 1 2 ! ( − x ) 2 + 1 3 ! ( − x ) 3 + ⋯ + 1 n ! ( − x ) n + ⋯ ) = 1 2 ( 2 + 2 2 !

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 11.6, Problem 13E

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To find: The Taylor series of the function f(x)=12(ex+e−x) at x=0 and give the interval of convergence for the series.

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Chapter 11.6, Problem 12E

Chapter 11.6, Problem 14E

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Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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The Taylor series of the function f ( x ) = 1 2 ( e x + e − x ) at x = 0 and give the interval of convergence for the series.

Solution Summary: The author explains how to find the Taylor series of the function f(x)=12

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To find: The Taylor series of the function f(x)=12(ex+e−x) at x=0 and give the interval of convergence for the series.

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Chapter 11 Solutions