Just let
Okay, so heres the problem:
Suppose is the function satisfying for all . Show that is continuous at .
Okay, this is my work so far:
We need to show , I started by figuring the value of . To find that value, I proceeded with:
Since:
and:
then:
but:
So we must have:
But we also have the restriction that:
Therefore it must be true that:
So, now i just need to show that:
but since ; we need only show:
This is where i'm stuck. I betting the answer is right under my nose, and is really obivous, and I'm just not seeing it. I appreciate any help that anybody can give.