The general form of L'Hôpital's rule covers many cases. Let and be extended real numbers (i.e., real numbers, positive infinity, or negative infinity). Let be an open interval containing (for a two-sided limit) or an open interval with endpoint (for a one-sided limit, or a limit at infinity if is infinite). The real valued functions and are assumed to be differentiable on except possibly at , and additionally formula_2 on except possibly at . It is also assumed that formula_6 Thus the rule applies to situations in which the ratio of the derivatives has a finite or infinite limit, but not to situations in which that ratio fluctuates permanently as gets closer and closer to .