Dirichlet Conditions: Does 1/(3-x) Satisfy (0,2pi)?

[thomas49th]

Homework Statement

I'm told these are

(1) f(x) is a periodic function;
(2) f(x) has only a finite number of finite discontinuities;
(3) f(x) has only a finite number of extrem values,

and I've got a function 1/(3-x) which I'm asked to give reasons why it doesn't satisfy the conditions in (0,2pi). I've plotted and at 3 it buggers off to infinity and pops back after x = 3. Which condition doesn't this satisfy. It's a discontinuity I know, but there is only one (finnite). Is it that it's not periodic? When the question says in (0,2pi) does that mean from that we're only looking at the function here

Thanks
Thomas

 

[Hurkyl]

Your f isn't a function on that interval, but that's easy to fix. I looked the conditions up on Wikipedia because I wasn't familiar with them by name -- the list there also includes the hypothesis that f is bounded.

Other sites have a different statement; among the others I saw were one that said the discontinuities were bounded, and one that said |f| is integrable over the interval (meaning, in particular, the integral is finite). I don't know the correct statement, or have thought it through to tell if they were all equivalent.