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

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ISBN: 9781305041264

Author: Tan

Publisher: CENGAGE C

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Chapter 11.6, Problem 17E

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To find: The Taylor series of the function f(x)=ln(1+x2) at x=0 and give the interval of convergence for the series.

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Chapter 11.6, Problem 16E

Chapter 11.6, Problem 18E

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Chapter 11 Solutions

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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 ) = ln ( 1 + x 2 ) 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)=mathrm

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To find: The Taylor series of the function f(x)=ln(1+x2) at x=0 and give the interval of convergence for the series.

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Chapter 11 Solutions