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.
出处
《江西理工大学学报》
CAS
2010年第3期69-73,共5页
Journal of Jiangxi University of Science and Technology
关键词
导函数
极限存在
单调
有界
连续可导
一致连续
derivative
limit exist
monotone
bounded
continuously differential
uniformly continuous
