# L'Hopital's rule.

Theorem 6.14.1   Let and be two functions verifying the following conditions:
1. The functions and are both differentiable on a pointed neighborhood of ;
2. ;
3. . Then .

Example 6.14.2   We can verify here some limits from Table 4.1:
(i)

(ii)

If , we can iterate the processus described in Theorem  14.1. For example:

Example 6.14.3

Generalization:

The result in Theorem 14.1 is unchanged if we replace by and .

Example 6.14.4

Remark 6.14.5   L'Hopital's rule can be proven, and generalized, using Taylor developments. This material is explained in next chapter.

Noah Dana-Picard 2007-12-28