how to show limit of $\frac{x^2-y^2}{x^3-y^3}$ as (x,y) goes to $(0,0)$ does not exist I know that $\lim\limits_{(x,y)\to (0,0)} \frac{x^2-y^2}{x^3-y^3}$ does not exist, but i'm not sure how to show it.
What I have done is let $y=kx$
and then,
$\lim\limits_{x\to 0} \frac{x^2-(k x)^2}{x^3-(kx)^3} = \lim\limits_{x\to 0} \frac{1-k^2}{x(1-k^3)}$
and k is just a constant,
is this enough to show that the limit does not exist?

Suppose $|k| \neq 1$,
Then the  expression is $$\frac{1-k^2}{1-k^3} \lim_{x \to 0} \frac1x$$
However, we know that $\lim_{x \to 0^+} \frac1x = \infty$ and $\lim_{x \to 0^-} \frac1x = -\infty$
