From my exam this morning:
Show that converges to f == 0 pointwise on [0, 1], but not uniformly.
There was some hint about going to 1/e or something like that.
I tried to let E > 0, using the definitions and whatnot, but it didn't seem to go anywhere! It was MUCH easier on the last test, when f_n was cos(x/n)...
Anywho... if you've got a solution, great. Otherwise, I'll post the answer in September after I've seen the prof again