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

7 (c).  Find  [Graphics:Images/ComplexFunLimitModHome_gr_305.gif]  as  [Graphics:Images/ComplexFunLimitModHome_gr_306.gif]  along the parabola  [Graphics:Images/ComplexFunLimitModHome_gr_307.gif].

Solution 7 (c).

See text and/or instructor's solution manual.

Answer.  [Graphics:../Images/ComplexFunLimitModHome_gr_308.gif].  

Solution.  A parameterization of the line is  [Graphics:../Images/ComplexFunLimitModHome_gr_309.gif],  and  [Graphics:../Images/ComplexFunLimitModHome_gr_310.gif]  as  [Graphics:../Images/ComplexFunLimitModHome_gr_311.gif]  along the parabola  [Graphics:../Images/ComplexFunLimitModHome_gr_312.gif]  is given by the limit   

        [Graphics:../Images/ComplexFunLimitModHome_gr_313.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunLimitModHome_gr_314.gif]

[Graphics:../Images/ComplexFunLimitModHome_gr_315.gif]


[Graphics:../Images/ComplexFunLimitModHome_gr_316.gif]

[Graphics:../Images/ComplexFunLimitModHome_gr_317.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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