Numerical Methods

Some equations cannot be solved algebraically. They can be solved by finding numerical approximations, by applying numerical methods. Numerical methods find improved approximations from existing ones.

Showing an equation has a root

For an equation $f(x)=0$, it can be shown that there is a root between $x=a$ and $x=b$ by showing that there is a sign change between $f(a)$ and $f(b)$. Also, this method can be used to show the accuracy of a root, by considering the error interval of a given root.

This method only works for continuous functions. If a function has an asymptote or other discontinuity, this method does not work.