Indeterminate Forms: L'Hospital's Rule

Suppose f(x) and g(x) are defined on some interval [a,b], such that f(a) = 0 and g(a) = 0, then the ratio f(x)/g(x) is not defined for x = a and gives a meaningless expression 0/0 but has a very definite meaning for values of x ≠ a.

Other indeterminate forms are of the types: ∞/∞, 0 . ∞, ∞ − ∞, 00, ∞0 and 1 respectively.

L'Hospital's Rule

Let f and g be continuous real valued functions defined on the closed interval [a,b], f, g be differentiable on (a,b) and g′(c) ≠ 0.

Using L'Hospital's Rule, evaluation of the limits of indeterminate forms works faster than conventional methods. 

All other indeterminate forms mentioned above can also be reduced to 0/0 or ∞/∞ by a suitable transformation.