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Putnam
1983 Putnam
A6
A6
Part of
1983 Putnam
Problems
(1)
limit of double integral with exp
Source: Putnam 1983 A6
9/14/2021
Let
F
(
x
)
=
x
4
exp
(
x
3
)
∫
0
x
∫
0
x
−
u
exp
(
u
3
+
v
3
)
d
v
d
u
.
F(x)=\frac{x^4}{\exp(x^3)}\int^x_0\int^{x-u}_0\exp(u^3+v^3)dvdu.
F
(
x
)
=
exp
(
x
3
)
x
4
∫
0
x
∫
0
x
−
u
exp
(
u
3
+
v
3
)
d
v
d
u
.
Find
lim
x
→
∞
F
(
x
)
\lim_{x\to\infty}F(x)
lim
x
→
∞
F
(
x
)
or prove that it does not exist.
calculus
integration
limits
real analysis