Question

define f(x,y)=xy^2/(x^2+y^2) prove that f

Answer 1

Is the function $ f(x,y)=xy/ (x^{2}+y^{2})$ where $f(0,0)$ is defined to be $0$ continuous? I don't think it is and I am trying to either show this by the definition or by showing that maybe a close set in $\mathbb{R}$ has an inverse set that is not closed in $ \mathbb{R} ^{2}$. I tried the point $0$ but this is open in $\mathbb{R}$ Any hints or ideas? Thanks !