Let me do that in a different color. So the change in the horizontal, that's this right over here. And then they're trying to find the limit as x approaches a. So as x gets closer and closer and closer and closer to a, what's going to happen is that when x is out here, we have this secant line. We're finding the slope of this secant line. But as x gets closer and closer, the secant lines better and better and better approximate the slope of the tangent line. Where the limit as x approaches a, but doesn't quite equal a, is going to be, this is actually our definition of our derivative, or I guess the alternate form of the derivative definition.