一类单调有界连续可微函数的导函数极限问题

Derivative Functions’Limit Problems for Monotone,Bounded and Continuously Differentiable Functions

本文基于文献给出的反例,知道了并不是所有单调有界且连续可微函数在x→时导函数的极限都为0。并且基于本文的定理,给出了能证明单调有界且连续可微函数在x→时导函数极限为0的两个充分条件。

Based on the counterexample given in literature,it is known that not all derivative functions of monotone,bounded and continuously differentiable functions have a limit of 0 when x→∞.Based on the theorem of this paper,two sufficient conditions are given to prove that the derivative functions of monotone,bounded and continuously differentiable functions have a limit of 0 when x→∞.