Basic Taylor Series

The Taylor series of a function about a pointis given by

Taylor series have many purposes, from approximating a function, allowing approximate solutions of equations to be found, in complex analysis, analysis, and many more areas. Taylor series can be multiplied or divided to find the Taylor series of products or quotients of functions, inverted to find the Taylor series of inverse functions, taken around many different points if the Taylor series about a point does not converge.

A Taylor series around the pointis also called a Maclaurin series.

Taylor series can be manipulated in some basic ways: