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insider the following function. f(x) = x¹/3, a = 1, n = 3, 0.9 ≤ x ≤ 1.1 a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = 20 162 (x-1)³- 4 18(x-1)²- 1(x-1) 3 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.) IR3(x)| ≤ 0.000012 x

insider the following function. f(x) = x¹/3, a = 1, n = 3, 0.9 ≤ x ≤ 1.1 a) Approximate f by a Taylor polynomial with degree n at the number a. T3(x) = 20 162 (x-1)³- 4 18(x-1)²- 1(x-1) 3 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.) IR3(x)| ≤ 0.000012 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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Mm.2.

Subject:- Advance mathematics 

Consider the following function. f(x) = x¹/3, a = 1, n = 3, 0.9 ≤ x ≤ 1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a. 20 4 T3(x) = 162 (x-1)³-18(x-1)²-¹(x-1) 3 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.) IR3(x)| ≤ 0.000012 X
Transcribed Image Text:Consider the following function. f(x) = x¹/3, a = 1, n = 3, 0.9 ≤ x ≤ 1.1 (a) Approximate f by a Taylor polynomial with degree n at the number a. 20 4 T3(x) = 162 (x-1)³-18(x-1)²-¹(x-1) 3 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.) IR3(x)| ≤ 0.000012 X
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