a. Explanation Given: The function f ( x ) = tan x and x = − 0.2 , − 0.1 , 0.0 , 0.1 , and 0.2 . The Taylor polynomials, p 1 ( x ) = x and p 3 ( x ) = x + x 3 3 . Calculation: Use the calculator to obtain the absolute error. The value of | tan x − p 1 ( x ) | computed as follows, x p 1 ( x ) tan x | tan x − p 1 ( x ) | −0.2 −0.2 − 0.2027 2.7100 × 10 − 3 −0.1 −0.1 − 0.1003 3.3467 × 10 − 4 0.0 0.0 0 0 0.1 0.1 0.1003 3.3467 × 10 − 4 0.2 0.2 0.2027 2.7100 × 10 − 3 The value of | tan x − p 3 ( x ) | computed as follows, x p 3 ( x ) = x + x 3 3 tan x | tan x − p 3 ( x ) | −0.2 ( − 0.2 ) + ( − 0.2 ) 3 3 = − 0.2027 − 0.2027 4.3369 × 10 − 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 89E

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 88E

Chapter 9.1, Problem 90E

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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 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