Consider the following function on $\frac{R^2}{0,0}$ :

$f(x,y)=\frac{x{y}^2}{2y^4+3x^2}$

$($a$)$ Evaluate $\underset{x0}{lim}f(x,y)$ along straight line paths $y=x,$ for $inR.$

$($b$)$ Show that $\underset{(x,y)(0,0)}{lim}f(x,y)$ does not exist.