3. Let f(г) — 1+х+z? + 23 + 4 + 25. (a) definition of Taylor polynomials. Find T3(x), the Taylor polynomial of f at x = 0 with degree 3 by using the (b) Find the remainder R3(x) = f (x) – T3(x). (c) Find the maximum value of f(4) (x) on the interval |x| < 0.1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.3: Change Of Basis
Problem 17EQ
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3. Let f(x) =1+x+x² + x³ + x4 + x³.
(a)
definition of Taylor polynomials.
Find T3(x), the Taylor polynomial of f at x = 0 with degree 3 by using the
(b)
Find the remainder R3(x) = f(x) – T3(x).
-
(c)
Find the maximum value of f(4) (x) on the interval |x|< 0.1.
(d)
the previous question.
Justify that Taylor's inequality holds true for R3(0.1) using your result from
Transcribed Image Text:3. Let f(x) =1+x+x² + x³ + x4 + x³. (a) definition of Taylor polynomials. Find T3(x), the Taylor polynomial of f at x = 0 with degree 3 by using the (b) Find the remainder R3(x) = f(x) – T3(x). - (c) Find the maximum value of f(4) (x) on the interval |x|< 0.1. (d) the previous question. Justify that Taylor's inequality holds true for R3(0.1) using your result from
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