Finite Differences

Approximating a derivative by setting a value for $\Delta x$, instead of integrating:

$$\frac{df(x)}{dx}=\underset{h\to 0}{\lim }\frac{f(x+h)-f(x)}{h}\approx \frac{f(x+\Delta x)-f(x)}{\Delta x}$$

Essentially, this is the difference between a tangent (the perfect analytical solution, touching the function at only one point) and a secant (the approximated numerical solution, touching the function at two points - preferably very close together, if accurate).