Numerical and Graphical Approximations
( a) Use the Taylor polynomials , , and for , centered at , to complete the table.

x

1

1.25

1.50

1.75

2

e x

e

3.4903

4.4817

5.7546

7.3891

P 1 ( x )

P 2 ( x )

P 4 ( x )

(b) Use a graphing utility to graph f ( x ) = e x and the Taylor polynomials in part (a).
(c) Describe the change in accuracy of polynomial approximations as the degree increases.

Question

Numerical and Graphical Approximations
( a) Use the Taylor polynomials , , and  for , centered at , to complete the table.





x


1


1.25


1.50


1.75


2




e x


e


3.4903


4.4817


5.7546


7.3891




P 1 ( x )

 
 
 
 
 



P 2 ( x )

 
 
 
 
 



P 4 ( x )

 
 
 
 
 




(b) Use a graphing utility to graph f ( x ) = e x and the Taylor polynomials in part (a).
(c) Describe the change in accuracy of polynomial approximations as the degree increases.

x	0	0.25	0.50	0.75	1
sin x	0	0.2474	0.4794	0.6816	0.8415
P 1 ( x )
P 3 ( x )
P 5 ( x )

x	0.25	0.50	0.75	1.00	1.50	2.00
F(x)
G(x)

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x	1	1.25	1.50	1.75	2
e x	e	3.4903	4.4817	5.7546	7.3891
P 1 ( x )
P 2 ( x )
P 4 ( x )