柯西中值定理的新证明及中值定理的两个应用

A New Proof of Cauchy Mean-value Theorem and Two Applications of Mean-value Theorem

基于柯西中值定理的一个新的证法,探讨了中值定理在求极限和涉及两个不同函数或者两个不同点的证明题中的应用,对进一步理解中值定理,掌握其应用具有一定意义。

This paper introduces a new proof of Cauchy mean-value theorem, and discusses the applications of mean-value theorem in calculating the limit and the proof of two different functions or two different points. It also discusses the importance to us for further understanding mean-value theorem and for gaining mastery in its applications.