推广的第一积分中值定理的逆问题及其渐近性  

On Inverse Problem of the Generalized First Mean Theorem for Integral and Its Approachability

作　　者：吴健荣[1] 谷建胜[1] 

机构地区：[1]苏州科技学院数学系,江苏苏州215009

出　　处：《西南师范大学学报（自然科学版）》2012年第8期19-23,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：江苏省高等教育教学教改研究课题"以提升学生职业能力为核心的师范教育实践教学体系的研究与实施"(2-3)

摘　　要：讨论了推广的第一积分中值定理的逆问题及其中值点的渐近性问题.首先应用变上限函数的技巧证明了该逆问题的存在性;然后利用L’Hospital法则和泰勒展开定理给出了中值点的渐近性结果.In this paper,the inverse problem of the generalized first mean-value theorem for the integral and its approachability of the mean-value have been discussed.First,by means of the technique of the integral function with a variable upper limit,the existences of the inverse problems of the generalized first mean-value theorems for the integrals have been proved.Then,thanks to L'Hospital Rules and Taylor's Theorem,the approachability results of the mean-value points have been given.

关 键 词：积分 中值定理 逆问题 渐近性 

分 类 号：O172.2[理学—数学]