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Mathematics
Mathematics
Problem
Let
g
g
g
be a function with Maclaurin series
g
(
x
)
=
1
−
2
x
+
3
x
2
+
⋯
g(x)=1-2x+3x^{2}+\cdots
g
(
x
)
=
1
−
2
x
+
3
x
2
+
⋯
and define
f
f
f
by
f
(
x
)
=
e
x
g
(
x
)
f(x)=e^{x}g(x)
f
(
x
)
=
e
x
g
(
x
)
. Determine
f
(
2
)
(
0
)
f^{(2)}(0)
f
(
2
)
(
0
)
.
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