Exercise 2.  Determine where the following functions are continuous.

2 (c).  .  

Solution 2 (c).

See text and/or instructor's solution manual.

Answer.  Continuous everywhere except at  .

Solution.    and the denominator is seen to be zero when  .   

Both   and   are continuous for all z and     when  .   

Therefore, by Theorem 2.4 the quotient    is continuous for all z except at  .  

Remark.  Later, using Definition 7.5, it will be seen that    is a removable singularity.

We are done.   

Aside.  We can let Mathematica double check our work.

Remark.  Later, using Definition 7.5, it will be seen that    is a removable singularity, and it's value will be  .

This solution is complements of the authors.

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