For a function to be continuous at a point, it has to be defined at that point, and the limit of the function approaching that point is equal to the value of the function at that point.

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