a. Explanation Given: The function f ( x ) = ( 1 + x ) − 1 2 . Calculation: The n th-order Tayler polynomial centered at a = 0 is as follows, p n ( x ) = f ( 0 ) + f ′ ( 0 ) 1 ! ( x ) + f ″ ( 0 ) 2 ! ( x ) 2 + ⋯ + f n ( 0 ) n ! ( x ) n (1) The value of f ( x ) = ( 1 + x ) − 1 2 and its derivatives at x = 0 as shown in the below table. n f n ( x ) f n ( 0 ) 0 f ( x ) = ( 1 + x ) − 1 2 f ( 0 ) = 1 1 f ′ ( x ) = − 1 2 ( 1 + x ) − 3 2 f ′ ( 0 ) = − 1 2 2 f ″ ( x ) = 3 4 ( 1 + x ) − 5 2 f ″ ( 0 ) = 3 4 Substitute 0 for n in equation (1) and obtain p 0 ( x ) b. To determine To sketch: The Taylor polynomial and the function.

Single Variable Calculus: Early Transcendentals & Student Solutions Manual, Single Variable for Calculus: Early Transcendentals & MyLab Math -- Valuepack Access Card Package

1st Edition

ISBN: 9780133941760

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Chapter 9.1, Problem 18E

To determine

To find: The nth-order Taylor polynomial centered at 0 and n=0,1,2.

To determine

To sketch: The Taylor polynomial and the function.

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Chapter 9.1, Problem 17E

Chapter 9.1, Problem 19E

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Chapter 9 Solutions

Single Variable Calculus: Early Transcendentals & Student Solutions Manual, Single Variable for Calculus: Early Transcendentals & MyLab Math -- Valuepack Access Card Package

Ch. 9.1 - Prob. 1QC Ch. 9.1 - Prob. 2QC Ch. 9.1 - Prob. 3QC Ch. 9.1 - Prob. 4QC Ch. 9.1 - Prob. 5QC Ch. 9.1 - In Example 7, find an approximate upper bound for...Ch. 9.1 - Suppose you use a second-order Taylor polynomial...Ch. 9.1 - Does the accuracy of an approximation given by a...Ch. 9.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 9.1 - Prob. 4E

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The nth-order Taylor polynomial centered at 0 and n = 0 , 1 , 2 .

Solution Summary: The author calculates the nth-order Taylor polynomial centered at a=0.

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To find: The nth-order Taylor polynomial centered at 0 and n=0,1,2.

To sketch: The Taylor polynomial and the function.

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Chapter 9 Solutions