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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

Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = x0
and then find the nth Taylor polynomial for the function in sigma
notation.
e"; xo = 3
Po(x) :
P1(x) =
P2(x)
P3(x)
PA(x)

Po(x) =
|P1(x)
p2(x) = [|
Choose one
n+1
ek
(x)
p3(x)
(k + 1): (" – 3)*
(x – e³)k=1
PA(x) = ||
e3
%3D
(x – 3)*
k=0
Σ
e3
(k + 1): (æ – e³)&+1
k=0
Pn(x)
+oo
e3
Σ
(k + 1)! (æ – e³)&+1
k=0
||
IM!

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