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

7 (e).  [Graphics:Images/AnalyticFunctionModHome_gr_233.gif].  

Solution 7 (e).

See text and/or instructor's solution manual.

Answer.   - 16.

Solution.  

                    [Graphics:../Images/AnalyticFunctionModHome_gr_234.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/AnalyticFunctionModHome_gr_235.gif]

[Graphics:../Images/AnalyticFunctionModHome_gr_236.gif]


[Graphics:../Images/AnalyticFunctionModHome_gr_237.gif]

[Graphics:../Images/AnalyticFunctionModHome_gr_238.gif]


                    [Graphics:../Images/AnalyticFunctionModHome_gr_239.gif]          [Graphics:../Images/AnalyticFunctionModHome_gr_240.gif]

  

                    The mapping  [Graphics:../Images/AnalyticFunctionModHome_gr_241.gif],  as  [Graphics:../Images/AnalyticFunctionModHome_gr_242.gif],  the image point  [Graphics:../Images/AnalyticFunctionModHome_gr_243.gif],

                    and we see that   limit   [Graphics:../Images/AnalyticFunctionModHome_gr_244.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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