Exercise 2.  Determine where the following functions are continuous.

2 (f).  .  

Solution 2 (f).

See text and/or instructor's solution manual.

Answer.  Continuous everywhere except at points on the unit circle  .  

Solution.    and the denominator is seen to be zero when  ,  i.e.  when  .   

Both   and   are continuous for all z and     when  .   

Therefore, by Theorem 2.4 the quotient    is continuous except at points on the unit circle  .  

This solution is complements of the authors.

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