Tangent as Limit of Secant

We can redefine Calculus as a branch of mathematics that enhances Algebra, Trigonometry, and Geometry through the limit process. Calculus simply will not exist without limits because every aspect of it is in the form of a limit in one sense or another. To illustrate this notion, consider a secant line whose slope is changing until it will become a tangent (or the slope of the curve) at point P (see figure below). Then we can say that the slope of the curve at any point P is the limit of the slope of the secant through P.