$\lim _{(x,y)\to(0,0)}\frac{x(x-y)}{x^4+y^4}$ does not exists Show that
$$\lim_{(x,y)\to(0,0)} \frac{xy(x-y)}{x^4+y^4}$$
does not exists.
I've tried the "traditional" paths, with $(x,x)$, $(0,x)$, $(0,-x)$, but I only get $0$ as answer. Any hint?
Thanks!

Hint: Consider the paths you've already taken together with the path $t\mapsto (t,t^2)$.
