advanced calculus demystified : ch. 2 - fundamentals of advanced calculus

Eg.              lim          f (x,y) = f (a,b)

            (x,y) -> (a,b)

-- Avoid points outside domain,like

 + Divison by zero (x/0)

 + Square roots of negative (-x^.5)

 + Logs of nonpositive numbers (log -x)

 + Tangents of odd multiples of π/2

In these case, function do not exist, and certainly not continuous. If exist, it may not have a limit. And if the function & the limit exist, the point may not be equal.