Exercise 9.  Limits involving  .  

The function     is said to have the limit  L  as  z  approaches  ,  and we write    iff
for every    there exists an    such that    (i.e., )  whenever  .  

Likewise,    iff   for every    there exists    such that  
  whenever    (i.e., ).

Use this definition to  

9 (b).  Show that  .  

Solution 9 (b).

See text and/or instructor's solution manual.

Solution.  Let    be given.    

Choose  .  

Suppose  .  

Then  ,  so    whenever  .

Therefore,  .  

This solution is complements of the authors.

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