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Mathematics
Problem
For
g
(
x
)
=
e
2
x
g(x)=e^{2x}
g
(
x
)
=
e
2
x
, what is the coefficient of
(
x
−
1
)
3
(x-1)^3
(
x
−
1
)
3
in the third-degree Taylor polynomial of
g
g
g
centered at
x
=
1
x=1
x
=
1
? a)
8
e
2
8e^{2}
8
e
2
b)
4
3
e
2
\dfrac{4}{3}e^{2}
3
4
e
2
c)
8
3
e
2
\dfrac{8}{3}e^{2}
3
8
e
2
d)
2
3
e
2
\dfrac{2}{3}e^{2}
3
2
e
2
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