So to show is continuous at , you first need to show that the function is defined at (easy, ), and then you need to show .
To do this, we need to prove . Working on the second inequality we have
Now if we restrict (say), since we have to make the distance from x small anyway, this gives
We need an upper bound for . Note that
Therefore, as long as we have , we have
So if we let and reverse the process, you will have your proof