Example 2.  The function     has a removable singularity at the point  .  

Solution 2.

Here we observe that "" is undefined.  The correct way to remove this singularity is to take the limit as  .

We can expand    in a Maclaurin series and then divide through by    to verify that this is correct.   
We can use Mathematica to obtain the first few terms in the series.

Or we can use Mathematica to find the first few terms of the Taylor series for .

(c) John H. Mathews 2005