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Linear Algebra: A Modern Introduction

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

(a) Find the Taylor polynomials up to degree 5 for f(x) = sin(x) centered at a = 0.
To(x)
=
T;(x)
T2(x) = ||
T3(x) =
T4(x) =
T5(x)
=
Graph f and these polynomials on a common screen.
AA A VA
1.0
1.0
1.0
0.5
0.5
0.5
-6
-4
-2
4
-4
|-2
4
6
-6
-4
4
6
0.5
-0.5
-0.5
1.0
-1.0
-1.0

1.0
0.5
-6
-4
-2
4
-0/5
71.0
(b) Evaluate f and these polynomials at x =
and n. (Round your answers to four decimal places.)
4' 2
To
I1 = T2
T3 = T4
T5
(c) Comment on how the Taylor polynomials converge to f(x).
As n increases, T,(x) is a good approximation to f(x) on a
Select---
v interval.

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