Show what you did. You asked several questions on convergence of series of functions. You surly had to learn something. Post what you did.
(1)
(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!