Taylor formula, also known as Taylor formula and Taylor mean value theorem, is an important theorem in advanced mathematics and an important test point in graduate mathematics. Its content is a formula that uses the information of a function at a certain point to describe the value near it.

If the function f(x) has a derivative up to (n+ 1) in the open interval (a, b) containing x0, the Taylor expansion can be used to approximate the original function.

Application of Taylor formula:

Taylor's mean value theorem (Taylor formula) can be used to prove the proposition that the mean value is equal or unequal.

Taylor formula can be used to prove functional equality or inequality on interval.

Taylor formula can be used for more accurate approximate calculation.

Taylor formula can be used to solve some limits.

Taylor formula can be used to calculate the value of higher derivative.