关于积分中值定理“中值ξ”的渐近性

ASYMPTOTIC PROPERTIES OF"THE MEAN VALUE ■"IN THE MEAN VALUE THEOREM FOR INTEGRAL

本文给出并证明了当 b→α时定积分中值定理中ξ将趋于α和 b 的中点,即■(ξ-α)/(b-α)=(1/2)。在 f^(i)(α)=0(i=1,2,…,n-1)且 f^((n))(α)≠0的条件下,还得到了■(ξ-α)/(b-α)=■(n>1)的结论。

This paper proved that ξ tends to the midpoint of a and b in the mean value theorem for integral as b■a,that is ■.Furthermore,The conclusion of ■ =■(n>1)is obtained from the conditions of f^(i)(a)=0(i=1,2,…,n-1)and (?)(a)≠0.