A limit with parameters

Task number: 3194

For which real numbers \(a>0\) and \(b>0\) does the limit

\[ \lim_{(x,y)\to(0{,}0)}\frac{|x|^a|y|^b}{x^2+y^2} \] exist, and what is it equal to?

  • Result

    The limit does not exist when \(a+b\le 2\), otherwise, it is equal to \(0\).

Difficulty level: Moderate task
Solution require uncommon idea
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