Explanation Definition used: If f be a function that can be differentiated n times at x = 0 . The Taylor polynomial of degree n for f at x = 0 is express as, P n ( x ) = f ( 0 ) + f ( 1 ) ( 0 ) 1 ! x + f ( 2 ) ( 0 ) 2 ! x 2 + f ( 3 ) ( 0 ) 3 ! x 3 + … + f ( n ) ( 0 ) n ! x n = ∑ i = 0 n f ( n ) ( 0 ) i ! x i where, f n is the n t h derivative of the function f . Calculation: In order to find the Taylor polynomial of degree 4 , use the first four derivative of f ( x ) evaluated at x = 0 as follows. Derivative of function f ( x ) Value of derivative at x = 0 f ( x ) = e − x f ( 0 ) = e − 0 = 1 f ( 1 ) ( x ) = − e − x f ( 1 ) ( 0 ) = − e − 0 = − 1 f ( 2 ) ( x ) = e − x f ( 2 ) ( 0 )

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

11th Edition

ISBN: 9780133886849

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 12.3, Problem 4E

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To find: The Taylor polynomial of degree 4 at x=0 for the given function f(x)=e−x.

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Chapter 12.3, Problem 3E

Chapter 12.3, Problem 5E

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Chapter 12 Solutions

Calculus With Applications, Books a la Carte Plus MyLab Math Package (11th Edition)

Ch. 12.1 - Find the first four terms of the sequence having...Ch. 12.1 - Prob. 2YT Ch. 12.1 - Prob. 3YT Ch. 12.1 - Prob. 4YT Ch. 12.1 - Prob. 5YT Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - List the first n terms of the geometric sequence...Ch. 12.1 - Prob. 5E

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The Taylor polynomial of degree 4 at x = 0 for the given function f ( x ) = e − x .

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To find: The Taylor polynomial of degree 4 at x=0 for the given function f(x)=e−x.

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Chapter 12 Solutions