单调性L’Hospital法则的扩展及应用  

Generalization of Monotone L’Hospital Rule and It’s Application

作　　者：韩淑霞[1,2] 王德荣[1,2] 黄永忠 HAN Shu-xia;WANG De-rong;HUANG Yong-zhong(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China;Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074 [2]华中科技大学工程建模与科学计算湖北省重点实验室,武汉430074

出　　处：《大学数学》2019年第4期94-99,共6页College Mathematics

基　　金：华中科技大学2018专项教学研究项目(201821);华中科技大学教研项目(2016050)

摘　　要：首先简化了单调性L’Hospital法则的形式,然后对此法则进行了几何解读,并在此基础上扩展了使用此法则的比值型函数类型.最后应用此法则改进或简化了多个例子中函数的单调性讨论及不等式证明.First of all,this paper simplifies the form of the Monotone L’Hospital Rule(MLR).Then a geometric interpretation of this law was made,and the basis of the interpretation,the type of ratio function that can use this rule is extended.Finally,this rule is used to improve or simplify the monotone discussion and inequality proof of functions in many examples.

关 键 词：单调性L’Hospital法则 单调性 不等式 

分 类 号：O172.2[理学—数学]