Question

lim (x,y)->(0,0) 2x^2-xy-2xy^2-y^3/2x-y

Answer 1

$L=\lim\limits_{(x,y)\to (0,0)}\dfrac{2x^2-xy-2xy^2-y^3}{2x-y}\\ \\ \\ L=\lim\limits_{(x,y)\to (0,0)}\dfrac{(2x-y)x-(2x-y)y^2}{2x-y}\\ \\ \\ L=\lim\limits_{(x,y)\to (0,0)}\dfrac{(2x-y)(x-y^2)}{2x-y}\\ \\ \\ \displaystyle L=\lim_{\substack{(x,y)\to (0,0)\\ (x,y)\neq (0,0)}}x-y^2\\ \\ \\ \boxed{L=0}$