Continuity of a piecewise function of two variable I'm given this equation:
$$
u(x,y) = 
\begin{cases}
\dfrac{(x^3 - 3xy^2)}{(x^2 + y^2)}\quad& \text{if}\quad (x,y)\neq(0,0)\\
 0\quad& \text{if} \quad (x,y)=(0,0).
\end{cases}
$$
It seems like L'hopitals rule has been used but I'm confused because


*

*there is no limit here it's just straight up $x$ and $y$ equals zero.

*if I have to invoke limit here to use Lhopitals rule, there are two variables $x$ and $y$. How do I take limit on both of them?


u(0,0) can't possibly exist as it would be a division by 0. You haven't given us enough information. What is the point of this equation? What is the problem you have to solve?
