Explanation Given information: The given function is f ( x ) = x 2 + 1 x + 1 at a = − 2 . Formula Used: We use the formula of the n t h Taylor polynomial centered at a of f ( x ) given by T n ( x ) = f ( a ) + f ' ( a ) 1 ! ( x − a ) 1 + f ' ' ( a ) 2 ! ( x − a ) 2 + ............. + f ( n ) ( a ) n ! ( x − a ) n Calculation: As the given function is f ( x ) = x 2 + 1 x + 1 and we need to take a = − 2 , thus T 2 ( x ) = f ( a ) + f ' ( a ) 1 ! ( x − a ) 1 + f ' ' ( a ) 2 ! ( x − a ) 2 = ( − 2 ) 2 + 1 − 2 + 1 + ( − 2 ) 2 + 2 ( − 2 ) − 1 ( − 2 + 1 ) 2 1 ! ( x − ( − 2 ) ) + 4 ( − 2 + 1 ) 3 2 ! ( x − ( − 2 ) ) 2 = 5 1 + 4 − 4 − 1 1 ( x + 2 ) + 4 − 2 ( x + 2 ) 2 = 5 − ( x + 2 ) − 2 ( x +

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ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 9.4, Problem 6E

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To Calculate:The T2,T3 polynomials for the given function centered at a=−2 .

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Chapter 9.4, Problem 5E

Chapter 9.4, Problem 7E

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Chapter 9 Solutions

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The T 2 , T 3 polynomials for the given function centered at a = − 2 .

Solution Summary: The author explains how to calculate the nth Taylor polynomials for the given function centered at a=-2.

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To Calculate:The T2,T3 polynomials for the given function centered at a=−2 .

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Chapter 9 Solutions