摘要
拉格朗日中值定理及柯西中值定理都是罗尔中值定理的推广。本文从其它角度归纳、推导了几个新的形式,拓宽了罗尔中值定理的使用范围。同时,用若干实例说明了微分中值定理在导数极限、导数估值、方程根的存在性、不等式的证明、以及计算函数极限等方面的一些应用。
The Lagrange mean-value theorem and the Cauchy mean-value theorem are extensions of the Rolle mean-value theorem.In this article,the Rolle mean-value theorem has been concluded and deduced in few more forms that helped to expand the use of the Rolle mean-value theorem.Also,the article has demonstrated of the application of differential mean-value theorem in derivative limit,derivative estimate value,existence of root of an equation,proof of inequality and calculation of functional limit upon many examples.
出处
《内蒙古农业大学学报（自然科学版）》
CAS
北大核心
2009年第3期207-212,共6页
Journal of Inner Mongolia Agricultural University(Natural Science Edition)
关键词
函数
连续
导数
微分中值定理
Function
continuous
derivative
differential mean-value theorem
