How to find $\lim_{(x,y)\rightarrow(0,0)} \frac{x^2\sin^2(y)}{x^2+3y^2}$ Find the following $$\lim_{(x,y)\rightarrow(0,0)}  \frac{x^2\sin^2(y)}{x^2+3y^2}$$
How to solve this limit? I have tried to use polar system, like sub everything with $x=rcos\theta$ and $y=\sin\theta$, but r cancel each other.

I think it means
$$0< \frac{x^2\sin^2y}{x^2+3y^2}< \frac{x^2y^2}{x^2+3y^2}<x^2$$
