Taylor Series

A special case of a power series where the coefficients are specifically derived from the function's derivatives at a particular point.

A representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

The Taylor series of a function $f(x)$ about a point $x = a$ is given by:

Where $f^{(n)}(a)$ is the $n$-th derivative of $f(x)$ evaluated at $x = a$. The higher the order of the derivative, the more accurate the approximation of the function around the point $x = a$.

Maclaurin series when the point of consideration is $x = 0$.