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. So let's start with a slightly different limit. Let me draw a line here actually. Let me draw a line just so we're doing something different. So let's take, let us take the limit as x approaches C of f of x, of f of x minus f of C. Of f of x minus f of C. Well can we rewrite this?