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Mathematics
Mathematics
Problem
If
f
(
x
)
f(x)
f
(
x
)
is a polynomial and if
lim
t
→
a
∫
a
t
f
(
x
)
d
x
−
(
t
−
a
)
2
(
f
(
t
)
+
f
(
a
)
)
(
t
−
a
)
3
=
0
for all
a
,
then the
\lim_{t \to a} \frac{\int_{a}^{t} f(x) dx - \frac{(t-a)}{2}(f(t) + f(a))}{(t-a)^3} = 0 \text{ for all } a, \text{ then the}
t
→
a
lim
(
t
−
a
)
3
∫
a
t
f
(
x
)
d
x
−
2
(
t
−
a
)
(
f
(
t
)
+
f
(
a
))
=
0
for all
a
,
then the
degree of
f
(
x
)
f(x)
f
(
x
)
can at most be a. 1 b. 2 c. 3 d. 4
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