Lagrange中值定理“中间点”的渐进性

Research into progressiveness of intermediate point of Lagrange mean value theorem

对Lagrange中值定理"中间点"的渐进性作了定性研究.通过对f(x)在(a,b)内低阶可导情形的研究,发现规律,即把f(x)在(a,b)内低阶可导可推广至n阶连续可导的情形,进而把正整数n推广到正实数m,并得到了更一般性的结论:lim ξ-a/b-a=(1/m+1)^(1/m) b→a.

This paper makes qualitative research on the progressiveness of the intermediate point of Largrange mean value theorem. By studying the situation of f（x） in （ a, b） low order derivableness, we found that f（x） in （a, b） low order derivative can be popularized to the situation of n order continuous derivableness, furthermore, that positive integer n can be popularized to positive real number m, a more generalized conclusion is arrived at：limb→a ζ-a/b-a=m√1/m＋1.