Answer
$\dfrac{1}{2}$
Work Step by Step
Solve the limit $\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x^2y-xy+4x^2-4x}$
$\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x(xy-y+4x-4)}=\lim\limits_{(x,y) \to (2,-4)} \dfrac{(y+4)}{x(x-1)(y+4)}$
Thus, $\dfrac{1}{2(2-1)}=\dfrac{1}{2}$
