a. Explanation Given: The function f ( x ) = cos 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 + x 4 24 . Calculation: Use the online calculator and obtain the absolute error. The value of | cos x − p 2 ( x ) | is shown in below Table. x p 2 ( x ) = 1 − x 2 2 f ( x ) = cos x | cos x − p 2 ( x ) | −0.2 1 − ( − 0.2 ) 2 2 = 0.98 cos ( − 0.2 ) = 0 .980066578 6 .66 × 10 − 5 −0.1 1 − ( − 0.1 ) 2 2 = 0.995 cos ( − 0.1 ) = 0 .995004165 4 .17 × 10 − 6 0.0 1 − ( 0 ) 2 2 = 1 1 0 0.1 1 − ( 0.1 ) 2 2 = 0.995 cos ( 0.1 ) = 0 .995004165 4 .17 × 10 − 6 0.2 1 − ( 0.2 ) 2 2 = 0.98 cos ( 0.2 ) = 0 .980066577 6 .66 × 10 − 5 The value of | cos x − p 4 ( x ) | is shown in below Table. x p 4 ( x ) = 1 − x 2 2 + x 4 24 f ( x ) = cos x | cos x − p 4 ( x ) | −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.

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

3rd Edition

ISBN: 9780134996103

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

Publisher: PEARSON

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Chapter 11.1, Problem 78E

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 11.1, Problem 77E

Chapter 11.1, Problem 79E

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Chapter 11 Solutions

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 11.1 - Verify that p3 satisfies p3(k)(a)=f(k)(a), for k =...Ch. 11.1 - Prob. 2QC Ch. 11.1 - Prob. 3QC Ch. 11.1 - Write out the next two Taylor polynomials p4 and...Ch. 11.1 - Prob. 5QC Ch. 11.1 - Prob. 6QC Ch. 11.1 - Suppose you use a second-order Taylor polynomial...Ch. 11.1 - Does the accuracy of an approximation given by a...Ch. 11.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 11.1 - Prob. 4E

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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.

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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 11 Solutions