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

7 (c).  [Graphics:Images/AnalyticFunctionModHome_gr_208.gif].

Solution 7 (c).

See text and/or instructor's solution manual.

Answer.   3.  

Solution.  

                    [Graphics:../Images/AnalyticFunctionModHome_gr_209.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/AnalyticFunctionModHome_gr_210.gif]

[Graphics:../Images/AnalyticFunctionModHome_gr_211.gif]


[Graphics:../Images/AnalyticFunctionModHome_gr_212.gif]

[Graphics:../Images/AnalyticFunctionModHome_gr_213.gif]

                      [Graphics:../Images/AnalyticFunctionModHome_gr_214.gif]          [Graphics:../Images/AnalyticFunctionModHome_gr_215.gif]

  

                    The mapping  [Graphics:../Images/AnalyticFunctionModHome_gr_216.gif],  as  [Graphics:../Images/AnalyticFunctionModHome_gr_217.gif],  the image point  [Graphics:../Images/AnalyticFunctionModHome_gr_218.gif],

                    and we see that   limit   [Graphics:../Images/AnalyticFunctionModHome_gr_219.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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