积分中值定理中“中间点”的渐近形态

ASYMPTOTIC BEHAVIOUR OF INTERMEDIATE POINT IN INTEGRAL THEOREM OF MEAN

本文讨论了当f(t)∈C^(n-1)[a,b],f^(l)(a)=0(i=1,2,…,n-1),f^n(a)存在且不为0(n≥1);g(t)∈c^(m-1)[a,b]g^j(a)=0(j=0,l,2,…,m-1),g^m(a)存在且不为0(m≥1)或g(t)∈c[a,b],g(a)≠0,g(t)或f^l(f)在[a,b]上不变号时,积分第一与第二中值定理中“中间点”的一般估计,即当x→a时,其中间点的渐近状态。

This paper obtaines when f(t)∈C^(n-1)[a, b], f^(i)(a) = 0 (i = 1, 2, ..., n--1),f^(n)(a) exists and f^(n)(a) ≠0 (n≥1); g(t) ∈C^(m-1) [a, b] g^(i) (a) = 0, (j= 0. 1, ...m-1), g^(m)(a)exists and g^(m) (a) ≠0(m≥1)or g(t)∈ C[a,b],g(a) ≠0, g(t)or f'(t) be invariant symbol in [a,b], general stimate of intermediate point in first integral and second integral theorem of mean. name- ly, when x→a, asymptopic behaviour of intermediate point ξ.