1.  Evaluate

.

2.  Verify that

.

3.  Verify that

.

4.  Let S be the square with vertices .  Show that is bounded on S.

5.  Let be such that along the square in problem 4) above

,

where M and k>1 and constants independent of N.  Prove that if are the poles of , then

.

6.  If a>0, show that

.

7.  If a>0, show that

.

(Hint: Use Problem 6.)

8.  Show that

.

9.  Let be such that along the square in problem 4) above

,

where M and k>1 and constants independent of N.  Prove that if are the poles of , then

.

10.  If a is a (real) number different from ,show that

.

11.  Prove that

(Hint: Consider, where S is the square with vertices .)