Continuity and differentiability

Hi all,

I got some problems doing some exams exercises...

They ask me to study the continuity and the differentiability of some functions but I always get similar results... (Doh)

$\displaystyle f(x,y)=x/(x-y^3)$, if $\displaystyle x$ != $\displaystyle y^3$

$\displaystyle f(x,y)=0$, if $\displaystyle x=y^3$

The function is continuous when $\displaystyle x$ != $\displaystyle y^3$ but it is not when $\displaystyle x=y^3$ because the limit for $\displaystyle (x,y)->(y^3,y)$ results +∞ or -∞ depending on the approaching direction... Am I wrong? If yes, how do I have to solve that limit? Thanks to all!