Recent content by metalbec

I'm struggling with something that I suspect is very basic. How do I should that the closure of a connected set is connected? I think I need to somehow show that it is not disconnected, but that's where I'm stuck. Thanks

This is a general question, I guess. If I am given an infinite series, how do I go about finding its sum using Fourier expansion?

Okay, I think I've done that. But I'm having a hard time grasping it. If I have already established that f'(0) does not exist, how did I just show that it is zero? Or does the fact that its limit is zero in itself show that it is discontinuous at 0?

Would I use the Pinching Theorem to show that because the limit as h approaches 0 from both sides is 0, then the limit of hsin (1/h) is also 0?

well. f(x)= x^2sin(1/x). I can define f(0) to be 0.

Hi. How do I show that f is differentiable, but f' is discontinuous at 0? I guess I'm just looking for a general idea to show discontinuity. Thanks