$(2)$ Is the function $f(x,y)=\{\begin{array}{ccc}\frac{x^{2}y}{x^2+y^2}& \text{f}\text{o}\text{r}(x,y)(0,& 0)\\ 1& \text{f}\text{o}\text{r}(x,y)=(0,& 0)\end{array}$ continuous at $(0,0)?$ Expalin.