Taylor formula is an important formula in calculus and an important tool for mathematical theory research and calculation. However, the application of Taylor formula is rarely introduced in most advanced mathematics textbooks, which makes it difficult for students to master Taylor formula and its application skills.

Because the low-order polynomial can't accurately represent the function and make approximate calculation, it is necessary to use high-order polynomial to approximate the function and give the corresponding error formula when some situations require high accuracy and need error estimation. Taylor formula is an important partial equation in mathematical analysis, so it has a high position in mathematics.