of certain functions R(x), we may come across the following situations like,

We say that they have the form of a number. But values cannot be assigned to them in a way that is consistent with the usual rules of addition and mutiplication of numbers. We call these expressions indeterminate forms. Although they are not numbers, these indeterminate forms play a useful role in the limiting behaviour of a function.

John (Johann) Bernoulli discovered a rule using derivatives to compute the limits of fractions whose numerators and denominators both approach zero or ∞. The rule is known today as L’Hôspital’s Rule, named after Guillaume de L’Hospital’s, a French nobleman who wrote the earliest introductory differential calculus text, where the rule first appeared in print.

The L'Hospital's Rule

Let f(x) and g(x) be differentiable functions and g'(x) ≠ 0.