From my exam this morning:

Show that $\displaystyle f_n(x) = nx(1-x)^n $ converges to f == 0 pointwise on [0, 1], but not uniformly.

There was some hint about $\displaystyle \frac{n}{n + 1}^n $ 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