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Consider the following function. f(x)=x8/7, a = 1, n = 3, 0.7 sxs 1.3 (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.) IR₂(x) s (c) Check your result in part (b) by graphing IR₂(x)\. y 0.00015 0.00010 0.00005 O 0.8 X 0.9 1.0 1.1 1.2 1.3 00 y -0.00005 -0.00010 -0.00015 X 08 0.9 1.0 1.1 TR 1.3 02 y -0.00005 -0.00010 -0.00015 1.2 1.3 0.00015 0.00010 NEV 0.00005 0.8 0.9 1.0 1.1 0.8 0.9 1.0 1.1 1.2 1.3 y

Consider the following function. f(x)=x8/7, a = 1, n = 3, 0.7 sxs 1.3 (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.) IR₂(x) s (c) Check your result in part (b) by graphing IR₂(x)\. y 0.00015 0.00010 0.00005 O 0.8 X 0.9 1.0 1.1 1.2 1.3 00 y -0.00005 -0.00010 -0.00015 X 08 0.9 1.0 1.1 TR 1.3 02 y -0.00005 -0.00010 -0.00015 1.2 1.3 0.00015 0.00010 NEV 0.00005 0.8 0.9 1.0 1.1 0.8 0.9 1.0 1.1 1.2 1.3 y

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, 0.7 ≤ x ≤ 1.3. (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)| ≤ (c) Check your result in part (b) by graphing IR,(x). y 0.00015 0.00010 0.00005 X 0.8 0.9 1.0 1.1 1.2 1.3 y -0.00005 -0.00010 -0.00015 O X 08 0.9 1.0 1.1 1.2 1.3 y -0.00005 -0.00010 -0.00015 0.8 0.9 11.0 1.1 1.2 1.3 X y 0.00015 ELV 0.00010 0.00005 X 0.8 0.9 1.0 1.1 1.2 1.3
Transcribed Image Text:Consider the following function. f(x) = x6/7, a = 1, n = 3, 0.7 ≤ x ≤ 1.3. (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)| ≤ (c) Check your result in part (b) by graphing IR,(x). y 0.00015 0.00010 0.00005 X 0.8 0.9 1.0 1.1 1.2 1.3 y -0.00005 -0.00010 -0.00015 O X 08 0.9 1.0 1.1 1.2 1.3 y -0.00005 -0.00010 -0.00015 0.8 0.9 11.0 1.1 1.2 1.3 X y 0.00015 ELV 0.00010 0.00005 X 0.8 0.9 1.0 1.1 1.2 1.3
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