## Proof of Taylor formula and exploration of its application

**YANG Xiong;Public Teaching Department, Loudi Vocational technical college;**

Taylor formula is an important part of Calculus, the content is abstract, students often difficult to understand and grasp,the main idea of Taylor formula is to use the “approximation method” to find the value of the function. In order to solve the problem that Taylor formula is difficult to understand, first of all, by explaining the approximate formula of the first derivative, we found that there were some problems in the accuracy of the calculation, thus leading to the Taylor formula, and carding its content, to clarify the connotation of Taylor's formula, and then to introduce its application in approximate calculation, limit calculation, equality proof, inequality proof and so on, so as to broaden the thinking of learning Taylor's formula and deepen the understanding of the formula, it is helpful for teaching and learning.

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