Hi guys, I've been trying to do this for a while but I'm not really getting anywhere. Hints would be much appreciated!
Prove that the function is continuous on , but cannot be defined at the origin in such a way that the resulting function is continuous on .
Just the first part for now - proving continuity on .
They want an proof. Here we go...
Then and we have:
Now I take the case where is such that and we have...
So it's proven for such (I think?)
Now I have no idea what to do about such that . Or was splitting it into two cases a bad idea? Am I going anywhere useful here?