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Consider the following function. f(x) = x6/7, 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) =

Consider the following function. f(x) = x6/7, 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) =

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) = x6/7, a = 1, n = 3, (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)| Enter a number. (c) Check your result in part (b) by graphing IR (X). -5.x 10 -6 y -0.000010 -0.000015 -0.000020 -0.000025 -0.000030 -0.000035 y 0.000035 0.000030 0.000025 0.000020 0.000015 0.000010 5.x 10 -6 0.9 0.9 0.8 ≤ x ≤ 1.2 1.0 1.0 1.1 1.1 1.2 1.2 X X 0.000035 0.000030 0.000025 0.000020 0.000015 0.000010 y -6 5.x 10 -5.x 10 y -6 -0.000010 -0.000015 -0.000020 -0.000025 -0.000030 -0.000035 0.9 0.9 1.0 1.1 1.1 X 1.2 1.2 X
Transcribed Image Text:Consider the following function. f(x) = x6/7, a = 1, n = 3, (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)| Enter a number. (c) Check your result in part (b) by graphing IR (X). -5.x 10 -6 y -0.000010 -0.000015 -0.000020 -0.000025 -0.000030 -0.000035 y 0.000035 0.000030 0.000025 0.000020 0.000015 0.000010 5.x 10 -6 0.9 0.9 0.8 ≤ x ≤ 1.2 1.0 1.0 1.1 1.1 1.2 1.2 X X 0.000035 0.000030 0.000025 0.000020 0.000015 0.000010 y -6 5.x 10 -5.x 10 y -6 -0.000010 -0.000015 -0.000020 -0.000025 -0.000030 -0.000035 0.9 0.9 1.0 1.1 1.1 X 1.2 1.2 X
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