L'Hôpital's theorem
The limit of a quotient can be calculated with l'Hôpital's rule
if the function in this point is indeterminate.
Explanation
We start from the function
of which we have determined that at the point a this function is indeterminate. Then you can try to approximate this point as a limit, so
This can be written in simplified form as
Now we play with the differentials du and dv, then we get
This seems like hocus pocus, but it immediately follows l'Hôpital's rule
HistoryThe name of this theorem is a tribute to the French mathematician Guillaume de l'Hôpital (1661 - 1704). |