Find d such that f(x) converges

EDIT: I see now to late that the title of the thread says: "Find d..." , but it is supposed to be: "Find c..."

Let:

The question is, what is c such that when

where k is some finite number.

Now what I did is something like this:

where

Now the only way such a limit is to converge to k is that x have equal powers, that is

, then .

Now the main problem is: How do I prove there is no other c that such that f(x) converges when ? I just need you to point me in the right direction.