Exercise 3.  State why   .  

Solution 3.

See text and/or instructor's solution manual.

Solution.  For the real functions    and    we have:

        ,  
    and
        .  

The result now follows by Theorem 2.1 since the real and imaginary parts of the last expression have limits that imply the desired conclusion.

          

Therefore    is continuous for all  .

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell