Applications of Taylor Series in Approximate Calculation and Limits

Abstract

Taylor series plays a significant role in mathematics, especially in the fields of mathematical analysis, calculus and applied mathematics. It is not only a theoretical tool, but also an indispensable method in practical applications. For instance, it plays an important role in the fields of physics, engineering and economics. Taylor function uses function which is represented by a series of infinite additive terms, which are calculated by the derivative of the function at a certain point. This paper mainly uses literature research method and empirical research method to introduce the basic information and practical application of Taylor series. Some methods are given to solve related problems. This article demonstrates a brief introduction of Taylor series, then illustrates the steps of proof for Taylor series and provides the solutions of several practical examples. In the end, the paper focuses on the application of Taylor series on limits and analyzes some typical and interesting examples.