Example 2.17.  Show that  .   

Solution.  We have  

              

Computing the limits for u and v, we obtain  

            ,  and
            
            ,  

so our previous theorem implies that .  

Explore Solution 2.17.

Enter the function f[z] and find the limit.

We can use Mathematica to make a mapping of a neighborhood of    in the z-plane and its image in the w-plane.

We see that  .  

(c) 2006 John H. Mathews, Russell W. Howell