please explain everything step by step 3. Let f(x) = 1+ x + x² + x³ + xª + 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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Answered: 3. Let f(x) = 1+x + x² + x³ + x“ + x5.…

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 + x“ + x5. (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 |æ| < 0.1.