15. Suppose a function f is approximated with a fourth-degree Taylor polynomial about x =1. If themaximum value of the fifth derivative between x = 1 and x = 3 is 0.01, that is, (5) (x) <0.01, thenthe maximum error incurred using this approximation to compute (3) is(A) 0.054(B) 0.0054(C) 0.26667(D) 0.02667(E) 0.00267

We have to calculate the maximum error incurred using approximation to compute f(3).

Answered: 15. Suppose a function f is…

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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Suppose that g(x) is a function that is continuous for all real values of x. Let's say that you want to compute the third-degree Taylor polynomial T3(x) centered at 8 for g(x), and you know that g(8) = 2, g' (8) = -5, g "(8) = 18, and g "(8) = 48. (In case you are having trouble reading the notation, I just gave you the value of g at 8, followed by the values of the first, second, and third derivatives of g at 8, in that order.) What is T3(x)?
10. (a) Produce the linear Taylor polynomials to f(x) = in (x) on 1 < x < 2, expanding about x, = }. Graph the error. Produce the linear minimax approximation to f(x) = ln (x) on [1, 2]. (b) Graph the error, and compare it with the Taylor approximation.
the function f(x) is a function with every order derivative in an open range containing x=1; the following table shows the values that the function f (x) and some of its derivatives take at the point x=1. Using these values, the approximate value of the number f(1,3) is central to X=1, which is 2. when we calculate the Taylor polynomial of order, which result is the following?
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f(x)=cos x-(x+1)2 function x=0 3. Calculate the Taylor polynomial b)If the above polynomial is used to calculate the value f(0.05), the absolute will occur and determine the relative error.
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