单调性L’Hospital法则的扩展及应用

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

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.