拉格朗日中值定理的应用

Application of the Lagrange Mean Value Theorem

该文分析和研究了拉格朗日中值定理的内容及其证明方法,对拉格朗日中值定理在证明不等式、证明等式以及求函数极限等方面的应用做了详细阐述.并通过实际例子展示了拉格朗日中值定理的应用技巧.

The Lagrange mean value theorem, also called the differential mean value theorem, can be applied not only to some mathematical theories, but also to a wide range of applications. This paper studies and analyzes the content of the Lagrange mean value theorem and its proof method, and expounds the applications of the Lagrange mean value theorem in proving inequality, proving equality and finding the limit of function. The method of inverse construction auxiliary function used in application is summarized to form a detailed and easy understanding of problem solving procedure, and the application technique of the Lagrange mean value theorem is demonstrated by practical examples.