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.