(1) Let .

(a) Find the pointwise limit of for all

(b) Is the convergence uniform on ?

(c) Is the convergence uniform on ?

(d) Is the convergence uniform on ?

(2) Let .

Find the pointwise limit of on . Is this convergence uniform on ? Is the convergence uniform on all of ?

(3) For each , find the points on where the function attains its maximum and minimum values. Use this to prove converges uniformly on . What is the limit function?

(4) For each , define on by

(a) Find the pointwise limit of on and decide whether or not the convergence is uniform.

(b)Construct an example of a pointwise limit of continuous functions that converges everywhere on the compact set to a limit function that is unbounded on this set.

If anyone can show me how to do these, I would appreciate it, thanks!