积分学第一中值定理“中间点”的渐近性研究新进展

对积分学第一中值定理的中间点当区间长度趋于零时的渐近性研究.新得到的结果不仅包含了过去若干已有结果,而且对涉及函数f(x),g(x)要求的条件几乎就是中值定理的,一个为连续,一个为可积不变号.

New Study on the Asymptoticity of the Intermediate Point in the First Mean Value Theorem for Integrals

Here's a study of the asymptoticity of the intermediate point in the first mean theorem for the integrals as the length of integral interval tends to zero.The new result consists not only of the results that already known,bus also the conditions that nearly relate to the function f(x)and g(x),which is the mean value theorem required:one is continuous,the other one is integrable and keeping sign.