Explanation Given information : f ( x ) = e − x + e − 2 x , at a = 0 , Formula used : The Taylor expansion formula as given below: f ( x ) ≃ f ( a ) + f ' ( a ) 1 ! ( x − a ) + f ' ' ( a ) 2 ! ( x − a ) 2 + f ' ' ' ( a ) 3 ! ( x − a ) 3 ............... f n ( a ) n ! ( x − a ) n ....... Calculation : The given function is f ( x ) = e − x + e − 2 x , a = 0 , Substitute the value and simplify f ( 0 ) = 2 Find the derivative of the given function f ' ( x ) = − e − x − 2 e − 2 x Substitute the value and simplify f ' ( 0 ) = − 3

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9.4, Problem 9E

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The Taylor polynomials T2 and T3 centered at x=0 for the function f(x)=e−x+e−2x .

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Chapter 9.4, Problem 8E

Chapter 9.4, Problem 10E

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Chapter 9 Solutions

Calculus - Standalone book

Ch. 9.1 - Prob. 1PQ Ch. 9.1 - Prob. 2PQ Ch. 9.1 - Prob. 3PQ Ch. 9.1 - Prob. 4PQ Ch. 9.1 - Prob. 5PQ Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E

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The Taylor polynomials T 2 and T 3 centered at x = 0 for the function f ( x ) = e − x + e − 2 x .

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The Taylor polynomials T2 and T3 centered at x=0 for the function f(x)=e−x+e−2x .

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Chapter 9 Solutions