Does $\displaystyle \left\{\begin{array}{lcl}0&:&y\leq 0\text{ or }y\geq x^2\\ \sin(\pi y/x^2)&:&0<y<x^2\end{array}\right.$ converge at $(0,0)$? [closed]

Question

determine whether $f(x,y)$ converges in $\mathbb{R}$ as $(x,y)\to (0,0)$ in $\mathbb{R}^{2}$. Justify the answer by quoting in full every theorem or exact reference for each.

$$f(x,y) = \begin{cases} 0 & \text{if }y\leq{0}\text{ or } y\geq{x^{2}}\\ \sin(πy/x^{2}) & \text{if}\,0<y<x^{2}\end{cases}$$