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Consider the following function. f(x)=x²/5, a=1, n-3, 0.9sxs 1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a 73(x) = 1 + (x-1)-25(x-1)²+15(x-1)³ (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) ≤ 0.00000268 x (c) Check your result in part (b) by graphing IR (x). -1.x10 -2x10 -3x10 -4x10 -5.x 10 3.x 10 4x10 495 1.00 1.07 TOL 0.95 1.05 1.10 -1.x10 -2x10 -3x10 -4x10 -5.x10 1.10 5.x10 4x10 3.x10 2x10 1.x10 0.95 1.00 1.05 1.10

Consider the following function. f(x)=x²/5, a=1, n-3, 0.9sxs 1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a 73(x) = 1 + (x-1)-25(x-1)²+15(x-1)³ (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) ≤ 0.00000268 x (c) Check your result in part (b) by graphing IR (x). -1.x10 -2x10 -3x10 -4x10 -5.x 10 3.x 10 4x10 495 1.00 1.07 TOL 0.95 1.05 1.10 -1.x10 -2x10 -3x10 -4x10 -5.x10 1.10 5.x10 4x10 3.x10 2x10 1.x10 0.95 1.00 1.05 1.10

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)=x²¹/5, 1, n=3, 0.9≤x≤1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a. T₂(x) = 1+ (x-1)-(x-1)²+15(x-1)3 (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.) R₂(x)| ≤ 0.00000268 x (e) Check your result in part (b) by graphing IR,(x). -1.x10 -2x10 -3x10 -4x10-6 -5.x10 6 5.x10 4x10 3x10 0.95 1/30 1.05 1.10 -1.x10 -2x10 -3x10 -4x10 -5.x10 20 095 1.00 1.05 1.10 5.x10 4x10 3x10 2x10 1.x10 0.95 1.00 1.05 1.10
Transcribed Image Text:Consider the following function. f(x)=x²¹/5, 1, n=3, 0.9≤x≤1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a. T₂(x) = 1+ (x-1)-(x-1)²+15(x-1)3 (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.) R₂(x)| ≤ 0.00000268 x (e) Check your result in part (b) by graphing IR,(x). -1.x10 -2x10 -3x10 -4x10-6 -5.x10 6 5.x10 4x10 3x10 0.95 1/30 1.05 1.10 -1.x10 -2x10 -3x10 -4x10 -5.x10 20 095 1.00 1.05 1.10 5.x10 4x10 3x10 2x10 1.x10 0.95 1.00 1.05 1.10
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