(a) Let Show that uniformly on At which points does the sequence of derivatives converge?
(b) Modify this example to show that it is possible for a sequence to converge uniformly but for to be unbounded.
(2) Consider the sequence of functions defined by .
(a) Show converges uniformly on and find . Show that is differentiable and compute for all
(b) Now show that converges on [0,1]. Is the convergence uniform? Set and compare and . Are they the same?
Thanks for any and all help!