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Putnam
2021 Putnam
A4
A4
Part of
2021 Putnam
Problems
(1)
Putnam 2021 A4
Source:
12/5/2021
Let
I
(
R
)
=
∬
x
2
+
y
2
≤
R
2
(
1
+
2
x
2
1
+
x
4
+
6
x
2
y
2
+
y
4
−
1
+
y
2
2
+
x
4
+
y
4
)
d
x
d
y
.
I(R)=\iint\limits_{x^2+y^2 \le R^2}\left(\frac{1+2x^2}{1+x^4+6x^2y^2+y^4}-\frac{1+y^2}{2+x^4+y^4}\right) dx dy.
I
(
R
)
=
x
2
+
y
2
≤
R
2
∬
(
1
+
x
4
+
6
x
2
y
2
+
y
4
1
+
2
x
2
−
2
+
x
4
+
y
4
1
+
y
2
)
d
x
d
y
.
Find
lim
R
→
∞
I
(
R
)
,
\lim_{R \to \infty}I(R),
R
→
∞
lim
I
(
R
)
,
or show that this limit does not exist.
Putnam
Putnam 2021