# Uniform convergence

1. May 4, 2006

### happyg1

Hi,
I'm studying for finals and I just need some feedback.
One of questions MIGHT be:
If I know a sequence of functions is pointwise convergent, how do I show that it's not uniformly convergent?
I think that a pointwise convergent sequence of functions might not converge to a continuous function, although it might.
Also, you can't interchange the limit and the derivitive, or the limit and the integral.
Am I right? Am I missing something?
Any feedback will be appreciated.
Thanks,
CC

2. May 4, 2006

### AKG

Find a counterexample. A standard example involves growing steeples, i.e. the nth function is 0 everywhere except on [2n,2n+2], say, and on this interval, it is basically an isoceles triangle with its value at 2n and 2n+2 being 0, and its value at 2n+1 being n, say.