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I want to find out the points, where the function

$f(x,y)=\dfrac{xy}{x-y}$ if $x\neq y$ and $f(x,y)=0$ otherwise, is continuous.

I have shown that at all the points $(x,y)$, where $x\neq y$, $f$ is continuous. Also at all those points $(x,y)\in \mathbb R^2\setminus \{(0,0)\}$ such that $x=y$, $f$ is not continuous. But what would happen at $(0,0)$? I couldn't do. Please give a hint.

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  • $\begingroup$ Please edit the question. Very first sentence in incomplete and giving no meaning $\endgroup$ – Dutta Dec 30 '13 at 2:58
  • $\begingroup$ Sorry! edited now @ Hopeless Fool $\endgroup$ – Anupam Dec 30 '13 at 2:59
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Hint: Let $(x,y)$ approach $(0,0)$ along the curve $x=t+t^2$, $y=t-t^2$. We can make the behaviour even worse by approaching along $x=t+t^3$, $y=t-t^3$.

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Hint: Check if the limit of $\frac{xy}{x-y}$ as $(x,y)\rightarrow (0,0)$ exists

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