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Problem 3
2021 CMC (Non-Math Major) Problem 3
2021 CMC (Non-Math Major) Problem 3
Source: 2021 CMC (Non-Math Major) Problem 3
November 25, 2022
calculus
Problem Statement
Let
f
(
x
)
f(x)
f
(
x
)
be a continuous function, where
f
(
0
)
≠
0
f(0)\neq0
f
(
0
)
=
0
. Find
lim
x
→
0
2
∫
0
x
(
x
−
t
)
f
(
t
)
d
t
x
∫
0
x
f
(
x
−
t
)
d
t
\lim_{x \to 0} \frac{2\int_{0}^{x}(x-t)f(t)dt}{x\int_{0}^{x}f(x-t)dt}
lim
x
→
0
x
∫
0
x
f
(
x
−
t
)
d
t
2
∫
0
x
(
x
−
t
)
f
(
t
)
d
t
.
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