- Take
and
; then we have
and

Here we have

and the function has two different infinite one-sided limits at 0. - 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.

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