Taylor formula is a very important technical tool in postgraduate mathematics, and limit is an essential knowledge point in postgraduate mathematics. Although there are many ways to do the limit, Taylor expansion is an essential one.

In the process of solving problems, we often encounter functions that look very complicated. At this time, using Taylor formula to expand will make the function solve skillfully and easily. In principle, any limit can be solved by Taylor formula, but the difference is simple and complicated.

The geometric meaning of Taylor formula is to approximate the original function with polynomial function. Because the polynomial function can be derived at any time, the calculation is simple, and it is easy to solve the extreme value or judge the nature of the function, so the information of the function can be obtained by Taylor formula. At the same time, for this approximation, error analysis must be provided to provide approximate reliability.