Let f(x) = (1+x) and x0-0.a) Find nth Taylor Polynomial Pa(x).b) The error bound (remainder term) on the upper limit of the interval [0,0.5] is(0.5)*+1. Find a value of n necessary for Pa(x) to approximate the function f(x)within 10$ on the said interval.

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Let f (x) = (1+x)"' and x0=0. a) Find nth Taylor Polynomial Pn(x).

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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Question

Let f(x) = (1+x) and x0-0.
a) Find nth Taylor Polynomial Pa(x).
b) The error bound (remainder term) on the upper limit of the interval [0,0.5] is
(0.5)*+1. Find a value of n necessary for Pa(x) to approximate the function f(x)
within 10$ on the said interval.

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