MathDB
Problems
Contests
Undergraduate contests
Putnam
1983 Putnam
A6
limit of double integral with exp
limit of double integral with exp
Source: Putnam 1983 A6
September 14, 2021
calculus
integration
limits
real analysis
Problem Statement
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.
Back to Problems
View on AoPS