When you have TWO variables, what matters is along which path you follow to get to that limit. ONLY if the limits exists along every path, and the limit is the same along every such path to the limit point can we say that the limit exists.
If the function is continuous at the point you're interested in, it is sufficient to apply limit() to any 1-dimensional path approaching that point. E.g., to find the limit of
as x,y-->0 you can take the 1-dimensional path x(t)=y(t)=t and reduce f to
Then, apply limit() to this 1D function of t as t-->0.
However, your example
is not continuous at x=y=0, so the limit is not defined there. Along x(t)=y(t)=t, the function converges to 1. If there is a particular path you know you are interested in, though, you could still apply limit() to that path.
Hope this helps!
DISCLAIMER: These are my own views and in no way depict those of MathWorks.