### Numerator and denominator have both a limit equal to 0 at the given point.

1. Take and ; then we have

 and

Here we have

and the function has two different infinite one-sided limits at 0.
2. Take and ; then we have

 and

Here we have

and the function has a limit at 0, which is equal to 0.

Possible method: Find a common factor in numerator and denominator, which pushes'' both towards 0, and cancel it.

Example 4.4.2   Find the limit at 3 of .

First, we compute separately the limit at 3 of the numerator and of tne denominator; we have:

Therefore, we have here an undeterminate case. Factorize niumerator and denominator:

It follows:

Noah Dana-Picard 2007-12-28