L'Hôpital's rule
Let
denote an
open interval,
and let
denote a point. Suppose that
-
are
continuous functions, which are
differentiable
on
, fulfilling
,
and with
for
.
Moreover, suppose that the
limit
-
![{\displaystyle {}w:=\operatorname {lim} _{x\rightarrow a}\,{\frac {f'(x)}{g'(x)}}\,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f2d126afd502f0a52ddcbc4233a8e1d1b749a537)
exists.
Then also the limit
-
exists, and it also equals
![{\displaystyle {}w}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a081b959224a8003fbaa26385f8c372743878767)
.