# Proving that a function is bounded

This is one part of an exercise in my homework, which for some reason I can't think of any way to prove.

$\displaystyle f(x,y)=\frac{xy^2}{x^2+y^4}$, if $(x,y)\neq (0,0)$ and $0$ otherwise.

I'm trying to prove that this function is bounded. I have figured that I only need to prove it for $x\geq 0$, since $f(x,y)=-f(-x,y)$, but I can't really get around to why this is bounded near $0$.

Thanks for the help.

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Have you tried letting $z=y^2$? –  Kimball Jun 8 '11 at 0:01

Hint: $(x-y^2)^2 \ge 0$ ${}{}{}{}{}{}{}{}{}$
+1. This is a really elegant hint. You might want to replace $>$ with $\ge$ –  user17762 Jun 8 '11 at 0:06