### 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). |