Exercise 7.  Use L'Hôpital's rule to find the following limits.

7 (a).  [Graphics:Images/AnalyticFunctionModHome_gr_182.gif].  

Solution 7 (a).

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/AnalyticFunctionModHome_gr_183.gif].  

Solution.  

                    [Graphics:../Images/AnalyticFunctionModHome_gr_184.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/AnalyticFunctionModHome_gr_185.gif]

[Graphics:../Images/AnalyticFunctionModHome_gr_186.gif]


[Graphics:../Images/AnalyticFunctionModHome_gr_187.gif]

[Graphics:../Images/AnalyticFunctionModHome_gr_188.gif]


                    [Graphics:../Images/AnalyticFunctionModHome_gr_189.gif]          [Graphics:../Images/AnalyticFunctionModHome_gr_190.gif]

  

                    The mapping  [Graphics:../Images/AnalyticFunctionModHome_gr_191.gif],  as  [Graphics:../Images/AnalyticFunctionModHome_gr_192.gif],  the image point  [Graphics:../Images/AnalyticFunctionModHome_gr_193.gif],

                    and we see that   limit   [Graphics:../Images/AnalyticFunctionModHome_gr_194.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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