Exercise 7.  Let  [Graphics:Images/ComplexFunLimitModHome_gr_278.gif].  

7 (a).  Find  [Graphics:Images/ComplexFunLimitModHome_gr_279.gif]  as  [Graphics:Images/ComplexFunLimitModHome_gr_280.gif]  along the line  [Graphics:Images/ComplexFunLimitModHome_gr_281.gif].  

Solution 7 (a).

See text and/or instructor's solution manual.

Answer.  [Graphics:../Images/ComplexFunLimitModHome_gr_282.gif].  

Solution.  A parameterization of the line is  [Graphics:../Images/ComplexFunLimitModHome_gr_283.gif],  and  [Graphics:../Images/ComplexFunLimitModHome_gr_284.gif]  as  [Graphics:../Images/ComplexFunLimitModHome_gr_285.gif]  along the line  [Graphics:../Images/ComplexFunLimitModHome_gr_286.gif]  is given by the limit   

        [Graphics:../Images/ComplexFunLimitModHome_gr_287.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunLimitModHome_gr_288.gif]

[Graphics:../Images/ComplexFunLimitModHome_gr_289.gif]


[Graphics:../Images/ComplexFunLimitModHome_gr_290.gif]

[Graphics:../Images/ComplexFunLimitModHome_gr_291.gif]

This solution is complements of the authors.

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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