©
0 1 2 3 4
-1
0
1
2
3
f(x)=x-1-0.5*sin(x)
0 1 2 3 4
0
0.2
0.4
0.6
0.8
1st Order Taylor Series Error
0 1 2 3 4
0
0.05
0.1
0.15
0.2
2nd/3rd Order Taylor Series Error
0 1 2 3 4
0
0.005
0.01
0.015
4th Order Taylor Series Error
©
First Derivative Approximations Compared to Theoretical
-4.0
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
x-values
f'(x)
Theoretical
Backward
Centered
Forward
Approximations of the 2nd Derivative
-15.0
-10.0
-5.0
0.0
5.0
10.0
15.0
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
x-values
f”(x)
f”(x)-Theory
f”(x)-Backward
f”(x)-Centered
f”(x)-Forward
©
©
©
