Let $f(x,y)=\frac{x^2}{x^2+y^2}si{n}^2(y)$ and $g(x,y)=\frac{x^{2}y}{x^4+y^2}.$ Show that

$($i$),\underset{(x,y)(0,0)}{lim}f(x,y)=0$ and

$($ii$),\underset{(x,y)(0,0)}{lim}g(x,y)$ does not exist.