Evaluate each limit$,$ or show that it does not exist.

$[6]($a$)\underset{(x,y)(1,4)}{lim}\frac{x^{2}y-4x^3}{y^2-xy-12x^2}$

$[6]($b$)\underset{(x,y)(0,0)}{lim}\frac{3x{y}^2}{x^{2}5y^4}$ non$-$existent $$ thy parabola

$[6]($c$)\underset{(x,y)(0,0)}{lim}\frac{x{y}^3}{(x^{2}2y^2{)}^{\frac{3}{2}}},($polar coordinates should be useful here$)$