The commonly used Taylor formula expansion is Fx=fx0/0! +f(x0)/ 1！ (x-x0)+f(x0)/2！ (x-x0)+...+f(x0)/n！ (x-x0)n power +Rn(x).
Application in advanced mathematics
In the theoretical research and application practice of higher mathematics, Taylor formula has a very important application, which can be summarized as follows:
(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.