Exercise 9.  Show that  

9 (a).   .

Solution 9 (a).

See text and/or instructor's solution manual.

Answer.   Use the same methods as in Exercise 11a of Section 5.1.

See text and/or instructor's solution manual.

Solution  Method I.   Use the Definition 5.5   .   

Then  ,  and we have  

                      

We are done.   

Aside.  We can let Mathematica check our work.

We are really done.   

Solution  Method II.   Using L'Hôpital's rule:

                      

We are really really 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