MacLaurin Series Approximation
MacLaurin series is a power series defined as:
...
!
6
)
0
(
!
5
)
0
(
!
4
)
0
(
'
'
'
'
!
3
)
0
(
'
'
'
!
2
)
0
(
"
)
0
(
'
)
0
(
!
)
0
(
)
6
(
6
)
5
(
5
4
3
2
0
)
(
+
+
+
+
+
+
+
=
∑
∞
=
f
x
f
x
f
x
f
x
f
x
xf
f
x
n
f
n
n
n
Finding the Maclaurin series involves 3 steps:
•
Determine the successive derivatives
•
Evaluate the function and the derivatives at
x = 0
•
Construct the series using the above definition
Below is a snapshot of some common Maclaurin series for your convenience.
You had seen how
e
x
was determined. As another example, we will do
sin(x)