a. Explanation Given: The function f ( x ) = sec x and x = − 0.2 , − 0.1 , 0.0 , 0.1 , and 0.2 . The Taylor polynomials, p 2 ( x ) = 1 + x 2 2 and p 4 ( x ) = 1 + x 2 2 + 5 x 4 24 . Calculation: Use the online calculator and obtain the absolute error. The value of | sec x − p 2 ( x ) | is shown in below Table 1. x p 2 ( x ) = 1 + x 2 2 f ( x ) = sec x | sec x − p 2 ( x ) | −0.2 1 + ( − 0.2 ) 2 2 = 1.02 sec ( − 0.2 ) = 1 .0203388 3.39 × 10 − 4 −0.1 1 + ( − 0.1 ) 2 2 = 1.005 sec ( − 0.1 ) = 1 .0050209 2.09 × 10 − 5 0.0 1 + ( 0 ) 2 2 = 1 1 0 0.1 1 + ( 0.1 ) 2 2 = 1.005 sec ( 0.1 ) = 1 .0050209 2.09 × 10 − 5 0.2 1 + ( 0.2 ) 2 2 = 1.02 sec ( 0.2 ) = 1 .0203388 3.39 × 10 − 4 Table 1 The value of | sec x − p 4 ( x ) | is shown in below Table 2. x p 4 ( x ) = 1 + x 2 2 + 5 x 4 24 f ( x ) = sec x | sec x − p 4 ( x ) | −0.2 1 + ( − 0.2 ) 2 2 + 5 ( − 0 b. To determine To describe: The error varying with x in each column and find the values of x largest and smallest in magnitude.

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

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

Publisher: PEARSON

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Chapter 9.1, Problem 85E

To determine

To approximate: The absolute error to two significant digits at the given points.

To determine

To describe: The error varying with x in each column and find the values of x largest and smallest in magnitude.

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Chapter 9.1, Problem 84E

Chapter 9.1, Problem 86E

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Chapter 9 Solutions

Calculus: Early Transcendentals (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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To approximate: The absolute error to two significant digits at the given points.

Solution Summary: The author calculates the absolute error to two significant digits at the given points using the online calculator.

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To approximate: The absolute error to two significant digits at the given points.

To describe: The error varying with x in each column and find the values of x largest and smallest in magnitude.

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Chapter 9 Solutions