Exercise 3.  Show that    provided  .  

Solution 3.

See text and/or instructor's solution manual.

Solution.  Using (6-8)   .  

Here we have    and   .


                       

We are assuming that    so we have    .

Also, the real functions   satisfy     .  

Thus, we can compute the following real limits  

                    ,

and we have    .  


                    ,

and we have    .  

Therefore,  

                    

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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