(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!