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 \(f\): \(f(x)=x^2\) \(f(x)=\frac{1}{3}e^x\) \(f(x)=\sin(2x^2)+x/4\)
Show secant line
\(h\) =
secant slope =
tangent slope =