Equivalently, the limit is L if for all paths that lead to P, the function also tends towards P. (Recall that for the one variable case we needed to check only the path from the left and from the r...Equivalently, the limit is L if for all paths that lead to P, the function also tends towards P. (Recall that for the one variable case we needed to check only the path from the left and from the right.) To show that a limit does not exist at a point, it is necessary to demonstration that two paths that both lead to P such that f(x,y) tends towards different values.