Hi guys, I've been trying to do this for a while but I'm not really getting anywhere. Hints would be much appreciated!
The problem
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
.
My attempt
Just the first part for now - proving continuity on
.
They want an
proof. Here we go...
Let
.
Let
.
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?
Please help!