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2007 IMS
5
Limit
Limit
Source: IMS 2007
May 18, 2007
limit
calculus
calculus computations
Problem Statement
Find all real
α
,
β
\alpha,\beta
α
,
β
such that the following limit exists and is finite:
lim
x
,
y
→
0
+
x
2
α
y
2
β
x
2
α
+
y
3
β
\lim_{x,y\rightarrow 0^{+}}\frac{x^{2\alpha}y^{2\beta}}{x^{2\alpha}+y^{3\beta}}
x
,
y
→
0
+
lim
x
2
α
+
y
3
β
x
2
α
y
2
β
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