The limit of the difference is the same thing as the difference of the limits. Well what's this thing over here going to be? Well f of C is just a number, it's not a function of x anymore, it's just f of C is going to evaluate to something. So this is just going to be f of C. This is just going to be f of C. So if the limit of f of x as x approaches C minus f of C is equal to zero. Well just add f of C to both sides and what do you get? Well you get the limit as x approaches C of f of x is equal to f of C. And this is the definition of continuity, the limit of my function as x approaches C is equal to the function, is equal to the value of the function at C. This is, this means that our function is continuous. Continuous at C. So just a reminder, we started assuming f differentiable at C, we use that fact to evaluate this limit right over here, which we got to be equal to zero.