1. Classify the singularities of each of the following functions:

a)  ,

b)  ,

c)  ,

d)  ,

e) .

2.    If has an isolated singularity at , show that cannot have a pole at  

3.  Let  be analytic in the punctured disk and has an essential singularity at .  Let w be a complex number.  Show that

is unbounded in any punctured disk .

(Compare to the proof of Weierstrass theorem.)