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Mathematics
Mathematics
Problem
Which of the following expresses the
n
n
n
th-degree Taylor polynomial
P
n
(
x
)
P_n(x)
P
n
(
x
)
of a differentiable function
f
f
f
about
x
=
a
x=a
x
=
a
? a)
P
n
(
x
)
=
∑
k
=
0
n
f
(
k
)
(
a
)
(
x
−
a
)
k
P_n(x)=\displaystyle\sum_{k=0}^{n} f^{(k)}(a)(x-a)^k
P
n
(
x
)
=
k
=
0
∑
n
f
(
k
)
(
a
)
(
x
−
a
)
k
b)
P
n
(
x
)
=
∑
k
=
0
n
f
(
k
)
(
a
)
k
!
x
k
P_n(x)=\displaystyle\sum_{k=0}^{n}\dfrac{f^{(k)}(a)}{k!}x^k
P
n
(
x
)
=
k
=
0
∑
n
k
!
f
(
k
)
(
a
)
x
k
c)
P
n
(
x
)
=
∑
k
=
0
n
f
(
k
)
(
a
)
k
!
(
x
−
a
)
k
P_n(x)=\displaystyle\sum_{k=0}^{n}\dfrac{f^{(k)}(a)}{k!}(x-a)^k
P
n
(
x
)
=
k
=
0
∑
n
k
!
f
(
k
)
(
a
)
(
x
−
a
)
k
d)
P
n
(
x
)
=
f
(
a
)
+
∑
k
=
1
n
f
(
k
)
(
a
)
k
(
x
−
a
)
k
P_n(x)=f(a)+\displaystyle\sum_{k=1}^{n}\dfrac{f^{(k)}(a)}{k}(x-a)^k
P
n
(
x
)
=
f
(
a
)
+
k
=
1
∑
n
k
f
(
k
)
(
a
)
(
x
−
a
)
k
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