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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 $z=y^2$?2011-06-08

1 Answers 1

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Hint: $(x-y^2)^2 \ge 0$ ${}{}{}{}{}{}{}{}{}$

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    It took me a second to see what you were getting at, but I really appreciate this hint. Nicely constructed.2011-06-08