   Chapter 11.11, Problem 7E

Chapter
Section
Textbook Problem

Find the Taylor polynomial T 3 ( x ) for the function f centered at the number a Graph f and T 3 on the same screen. f ( x ) = ln x ,     a = 1

To determine

To find:

The Taylor polynomial T3(x) for the function f centred at the number  a and then to graph f and T3(x)

Explanation

1) Concept:

The Taylor polynomial centred at a is

Tnx=i=0nfiai!x-ai

=f0a0!x-a0+fa1!x-a+f2a2!x-a2+f3a3!x-a3+

2) Given:

The function fx=lnx, a=1

3) Calculation:

fx=lnx

Therefore,

f0x=lnx and f0a=lna

f1x=1x and f1a=1a

f2x=-1x2 and f2a=-1a2

f3x=2x3 and f3a=2a3

For a=1,  i=3 the Taylor polynomial T3(x) for the function fx=lnx

T3x

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