MATH 5321
Exam II
Make-Up
1 April 2009
Answer the problems on separate paper. You do not need to rewrite the problem statements on
your answer sheets. Work carefully. Do your own work. Show all relevant supporting steps!
1.
X
2.
X
3. (20 pts)
Find the number of zeros of
a.)
b.)
c.)
4. (20 pts)
p ( z ) = z 6 − 6 z 4 − 10 z − 2
in B(0,1)
in B(0,2)
in B(0,3)
Let G be a bounded region in ^ . Let { f n } ⊂ C (G , ^ ) ∩ A (G ) and let
f ∈C (G , ^ ) ∩ A (G ) . Suppose that f n → f uniformly on ∂G . Show
that f n → f in C (G , ^ ) .