Finding the slope of a tangent line as a limit of secant lines.
The tangent line problem is the first big goal of Calculus: finding the slope of a tangent line to a function f(x) at x=a.
To tackle the tangent line problem, we start with the slope of a secant line on the interval [a,x]. We take the limit as x approaches a, and we see that the slope of the secant line approaches the slope of the tangent line, given us the slope of a tangent line formula limit as x goes to a of (f(x)-f(a))/(x-a).
