Show discontinuity of $\frac{xy}{x^2+y^2}$ How to show this function's discontinuity?
$ f(n) = \left\{ 
   \begin{array}{l l}
     \frac{xy}{x^2+y^2} & \quad , \quad(x,y)\neq(0,0)\\
     0 & \quad , \quad(x,y)=(0,0)
   \end{array} \right.$

HINT: Let $f$ approach $(0,0)$ along $y=x$, so $f=\frac{x^2}{2x^2}=\frac{1}{2}$ along $y=x$
