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Consider the following function. f(x) = x3/5, a = 1, n= 3, 0.8 Sxs 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) z Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| S (c) Check your result in part (b) by graphing |R,(x)|.

Consider the following function. f(x) = x3/5, a = 1, n= 3, 0.8 Sxs 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) z Tn(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| S (c) Check your result in part (b) by graphing |R,(x)|.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following function. F(x) = xP, a = 1, n = 3, 0.8 < x < 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(X) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) × T,(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| < (c) Check your result in part (b) by graphing |R,(x)|. y y 0.00008 0.9 1.0 1.1 1.2 -0.00002 0.00006 -0.00004 0.00004 -0.00006 0.00002 -0.00008 X 0.9 1.0 1.1 1.2 y y 0.9 1.1 1.2 0.00008 -0.00002 0.000061
Transcribed Image Text:Consider the following function. F(x) = xP, a = 1, n = 3, 0.8 < x < 1.2 (a) Approximate f by a Taylor polynomial with degree n at the number a. T3(X) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) × T,(x) when x lies in the given interval. (Round your answer to eight decimal places.) |R3(x)| < (c) Check your result in part (b) by graphing |R,(x)|. y y 0.00008 0.9 1.0 1.1 1.2 -0.00002 0.00006 -0.00004 0.00004 -0.00006 0.00002 -0.00008 X 0.9 1.0 1.1 1.2 y y 0.9 1.1 1.2 0.00008 -0.00002 0.000061
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