Let f(x) = 1+ x + x² + x³ + xª + x5. (a) (". .) Find T3(x), the Taylor polynomial of f at x = 0 with degree 3 by using the definit ion of Taylor polynomials. (b) ) Find the remainder R3(x) = f(x) – T3(x). (c) ...k) Find the maximum value of f(4)(x) on the interval |x|< 0.1. (d) Pe) Justify that Taylor's inequality holds true for R3(0.1) using your result from the previous question.

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