### Numerator and denominator have both an infinite limit at the given point.

1. Take and ; then we have

 and

Here we have

and

2. 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 Dana-Picard 2007-12-28