(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!