L'Hôpital's rule
You can calculate the limit of a quotient using L'Hôpital's rule
if the function in this point is indefinite.
Explanation
You may even repeat this rule several times to get a useful result. You may use l'Hôpital's rule only if it is necessary to get a correct result. This sounds rather strange, but in practice it works well.
Example 1
A simple limit is
Example 2
A simple limit is
Example 3
A logarithm is a limit because
Example 4
A limit with the sinc function is
Example 5
Example 6
A limit with the sine can be solved directly
If you use l'Hôpital's rule here it goes wrong, because
.gif){kind=small}
and that is not correct.