And then you could even look at a, you could look at a function that is truly continuous. If you look at a function that is truly continuous, so something like this. Something like this. That is x equals C. Well, this is f of C. This is f of C. And if you were to take the limit as x approaches C, as x approaches C from either side of f of x, you're going to approach f of C. So here you have the limit as x approaches C of f of x indeed is equal to f of C. So it's what you would expect for a continuous function. So now that we've done that review of differentiability and continuity, let's prove that differentiability actually implies continuity. And I think it's important to kind of do this review just so that you can really visualize things. So differentiability implies this, this limit right over here exists.