If $f:\mathbb R^2\to \mathbb R$ is given by $f(x,y) = \left\{ \begin{array}{cc} [\frac{\sin x}{x}]+[\frac{y}{\sin y}] & \mbox{if } xy \neq 0 \\ 2 & \mbox{if } xy = 0 \end{array} \right.$
Is the function continuous at $(0,0)$. $[.]$ denotes the greatest integer function.
I am on the opinion that the function is discontinuous there at but couldn't find the suitable sequence to show that. Please help!