a. Explanation Given: The function f ( x ) = sin − 1 x . Result used: The n th-order Tayler polynomial centered at a is as follows, p n ( x ) = f 0 ( a ) 0 ! ( x − a ) 0 + f ′ ( a ) 1 ! ( x − a ) 1 + f ″ ( a ) 2 ! ( x − a ) 2 + ⋯ + f n ( a ) n ! ( x − a ) n 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 ) = sin − 1 x and its derivatives at x = 0 as shown in the below table. n f n ( x ) f n ( 0 ) 0 f ( x ) = sin − 1 x f ( 0 ) = 0 1 f ′ ( x ) = 1 1 − x 2 b. To determine To sketch: The Taylor polynomial and the function.

Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)

2nd Edition

ISBN: 9780321977298

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

Publisher: PEARSON

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Chapter 9.1, Problem 22E

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 21E

Chapter 9.1, Problem 23E

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Chapter 9 Solutions

Calculus: Early Transcendentals, Books a la Carte Plus MyLab Math/MyLab Statistics Student Access Kit (2nd Edition)

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 Ch. 9.1 - How is the remainder Rn(x) in a Taylor polynomial...Ch. 9.1 - Explain how to estimate the remainder in an...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...Ch. 9.1 - Linear and quadratic approximation a. Find the...

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

Solution Summary: The author calculates the n th-order Tayler 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