Consider the following function. f (x) = x/", 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) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f - Tn(x) when x lies in the given interval. (Round the answer to eight decimal places.)
Consider the following function. f (x) = x/", 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) = (b) Use Taylor's Inequality to estimate the accuracy of the approximation f - Tn(x) when x lies in the given interval. (Round the answer to eight decimal places.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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
Transcribed Image Text:Consider the following function.
f (x) = x/7, 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) =
(b) Use Taylor's Inequality to estimate the accuracy of the approximation f × Tn(x) when x lies in the given interval.
(Round the answer to eight decimal places.)
|R3(x)| <
(c) Check your result in part (b) by graphing |Rn(x)|. (Do this on your graphing device. Your instructor may ask to
see this graph.)
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