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# what is L'Hopital's Rule?

12 years ago

L'Hospital's Rule is as follows:

Let f and g be functions that are differentiable on an open interval (a, b) containning c, except possibly at c itself. Assume that g'(x) does not = 0 for all x in (a, b), except possibly at c itself. If the limit of f(x)/g(x) as x approaches c produces the indeterminate for 0/0, then

lim    f(x) = lim    f '(x)
x-->c  g(x)     x-->c  g '(x)

provided the limit on the right exists or is infinite. This result also applies if the limit of f(x) / g(x) as x approaches c produces any one of the indeterminate forms infinity/infinity, (- infinity)/infinity, infinity/(- infinity), or (- infinity)/(- infinity). Note that you do not apply the quotient rule! The rule above utilizes f '(x) / g '(x) and not the derivative of f(x) / g(x).