(a) Find the polynomial whose value and slope agree with the value and slope of at the point .
(b) Find the polynomial whose value and first two derivatives agree with the value and first two derivatives of at the point . This polynomial is called the second-degree Taylor polynomial of .
(c) Complete the table comparing the values of . What do you observe?
x
-1.0
-0.1
-0.001
0
0.001
0.1
1.0
cos x
P 2 ( x )
(d) Find the third-degree Taylor polynomial of f ( x ) = sin x at x = 0 .
