For c a real number, if
limx → cf(x) = 0andlimx → cg(x) = 0
limx → cf(x)/g(x) = limx → cf'(x)/g'(x)
provided that the second limit exists or is ∞ or -∞.
The first version of L'Hopital's rule remains valid if the symbol x → c is replaced everywhere it occurs with one of the following symbols:
Version 1 and 2 of L'Hopital's rule for the indeterminate form 0/0 are also valid if the limit of f and the limit of g are both infinite; that is, both +∞ and -∞ are permissible for either limit.