Exercise 5.  Show that

5 (a).  [Graphics:Images/ComplexFunLimitModHome_gr_182.gif].  

Solution 5 (a).

See text and/or instructor's solution manual.

Solution.  We can simplify as follows:

        [Graphics:../Images/ComplexFunLimitModHome_gr_183.gif]  

Aside.  If you forgot the tricky substitution  [Graphics:../Images/ComplexFunLimitModHome_gr_184.gif],  it's o.k. to use the calculation  

        [Graphics:../Images/ComplexFunLimitModHome_gr_185.gif]  

And we find that

        [Graphics:../Images/ComplexFunLimitModHome_gr_186.gif]  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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