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Mathematics
Mathematics
Problem
For a function
f
f
f
that possesses derivatives of all orders at
x
=
a
x=a
x
=
a
, which expression equals the coefficient of the
(
x
−
a
)
n
(x-a)^n
(
x
−
a
)
n
term in the degree–
n
n
n
Taylor polynomial for
f
f
f
about
x
=
a
x=a
x
=
a
? a)
f
(
n
)
(
a
)
f^{(n)}(a)
f
(
n
)
(
a
)
b)
f
(
n
)
(
x
)
n
!
\dfrac{f^{(n)}(x)}{n!}
n
!
f
(
n
)
(
x
)
c)
f
(
n
)
(
a
)
n
!
\dfrac{f^{(n)}(a)}{n!}
n
!
f
(
n
)
(
a
)
d)
f
(
n
)
(
a
)
n
!
f^{(n)}(a)\,n!
f
(
n
)
(
a
)
n
!
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