TITLE: Proving that a function is bounded
QUESTION [5 upvotes]: 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.

REPLY [7 votes]: Hint:  $(x-y^2)^2 \ge 0$ ${}{}{}{}{}{}{}{}{}$