一类单调有界光滑函数的导函数极限存在性  

The Limit Existence of Derivative of Some Functions with Monotone Bounded and Continuously Differential

作　　者：范丽君[1] 郭挺[1] 

机构地区：[1]江西理工大学理学院,江西赣州341000

出　　处：《江西理工大学学报》2010年第3期69-73,共5页Journal of Jiangxi University of Science and Technology

摘　　要：凭直觉,似乎函数f(x)在单调、有界、连续可微的条件下,能有limf′x→∞(x)=0的结论,然而这是一个错觉,本研究为此构造了一个反例.但是函数若添加条件——f′(x)一致连续,或添加条件——f″(x)在R上有界,则可以得出limf′x→∞(x)=0的结论.By intuition,it seems that under the condition that f（x）is monotone,bounded and continuously differential,it may follow that limf′x→∞（x）=0.However,this is a misconception.A concrete example is presented to prove it in the article.When f′（x）is uniformly continuous,or f″（x）is bounded in R,it follows that limf′x→∞（x）=0.

关 键 词：导函数 极限存在 单调 有界 连续可导 一致连续 

分 类 号：O172.1[理学—数学]