Taylor formula is named after British mathematician Brook Taylor, who first described it in a letter 17 12. Taylor formula is one of the commonly used approximate methods to study the properties of complex functions, and it is also an important application content of function differential calculus.

Taylor formula is a very important content in advanced mathematics. It approximately represents some complex functions as simple polynomial functions. This function of Taylor formula makes it a powerful tool to analyze and study many mathematical problems.

Application of Taylor formula

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

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

(3) Taylor formula can be used for more accurate approximate calculation.

(4) Taylor formula can be used to solve some limits.

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

The above contents refer to Baidu Encyclopedia-Taylor formula.