l'Hospital's rule applies to many limits of indeterminate form 0/0 or ∞/∞. Specifically, if the limit of the numerator and denominator are both 0 or are both infinity, then the limit of f(x)/g(x) is the limit of f'(x)/g'(x), provided that the latter limit exists or is infinite. This is useful if the limit of f'(x)/g'(x) is easy to compute. Sometimes you may need to apply the rule repeatedly, or to do some algebraic manipulation before applying the rule.