Numerator and denominator have both an infinite limit at the given point.
 Take
and
; then we have
and 

Here we have
and
 Take
and
; then we have
and 

Here we have
and the function
has a limit at
, which is equal to
.
Possible method: Find a common factor in numerator and denominator, which ``pushes'' both towards infinity, and cancel it.
Example 4.4.3
Find the limit at
of
.
We can easily show that
and 

thus we have an undeterminate case.
Let us write
in a more suitable form:
As
and
we obtain that
In fact we saw here an example of what is explained extensively for rational functions in subsection 5.1.
Noah DanaPicard
20071228