n重积分中值定理中值点的渐近性

Asymptotic Properties of Mean of Point of Mean Value Theorem on n-fold Integrals

给出了n重积分正则中值点的概念,用罗比塔法则推得了当积分区域收缩于某定点时,n重积分正则中值点的渐近性,并对积分区间长度趋于无穷时二重积分中值定理中值点的渐近性进行了讨论.

The concept of the regular point of mean value on n -fold integrals is introduced. By L＇Hospital Principle, the asymptotic properties of the regular point of mean value on n - fold integrals are discussed when integral region tends to some fixed point. In particular, the asympotic characteristic of point of mean value on 2 - fold integrals is investigated when integral region tends to ＋∞.