Does the approach [here](https://math.stackexchange.com/a/3273950/94817) to show that $\begin{equation}
f(x,y) =
\begin{cases}
\frac{x^3+y^3}{x-y} &x\neq y\\
0 &x = y
\end{cases}
\end{equation}$ is discontinuous at origin, that is going along path $y=mx^{1/3}$ really work?