Calculus consists of those problems in mathematics that can be solved with the following basic approach:

Approximate and take a limit!

The simplest, standard, geometric example of this process is the approximation of the slope of a tangent line with a secant line. Here's an illustration of this basic idea.

Choose

f

f (x) = x^{2}

f (x) = \frac{1}{3} e^{x}

f (x) = \sin (2 x^{2}) + x / 4

Show secant line

h

secant slope =

tangent slope = 0.80