using maclaurin series expand XCosecX
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Step-by-step explanation:
We have:
f
(
x
)
=
x
sin
x
First let us take a look at the graph and see how "well defined" the function is:
graph{x/sinx [-40, 40, -20, 20]}
The Maclaurin series can be expressed in the following way:
f
(
x
)
=
f
(
0
)
+
f
'
(
0
)
1
!
x
+
f
'
'
(
0
)
2
!
x
2
+
f
'
'
'
(
0
)
3
!
x
3
+
(
f
(
4
)
)
0
4
!
x
4
+
...
=
∞
∑
n
=
0
f
(
n
)
(
0
)
n
!
x
n
We also note from the graph that
f
is even, so we expect all odd powers of
x
in the series to vanish. So, Let us find the derivatives, and compute the values at
x
=
0
.
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