a. Explanation Given: The function f ( x ) = ln ( 1 + x ) and x = − 0.2 , − 0.1 , 0.0 , 0.1 , and 0.2 . The Taylor polynomials, p 1 ( x ) = x and p 2 ( x ) = x − x 2 2 . Calculation: Use the online calculator and obtain the absolute error. The value of | ln ( 1 + x ) − p 1 ( x ) | computed as follows, x ln ( 1 + x ) p 1 ( x ) = x | ln ( 1 + x ) − p 1 ( x ) | −0.2 −0.2231 −0.2 2.3143 × 10 − 2 −0.1 −0.1054 −0.1 5.3605 × 10 − 3 0.0 0 0.0 0 0.1 0.0953 0.1 4.6898 × 10 − 3 0.2 0.1823 0.2 1.7679 × 10 − 2 The value of | ln ( 1 + x ) − p 2 ( x ) | computed as follows, x p 2 ( x ) = x − x 2 2 ln ( 1 + x ) | ln ( 1 + x ) − p 2 ( x ) | −0.2 ( − 0.2 ) − ( − 0.2 ) 2 2 = − 0.22 −0.2231 3.1436 × 10 − 3 −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 88E

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 87E

Chapter 9.1, Problem 89E

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Calculus: Early Transcendentals (2nd Edition)

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

Solution Summary: The author explains how to approximate the absolute error to two significant digits at the given points.

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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