不同形式的泰勒定理及其应用  

On Different Types of Taylor Theorems and Their Applications

作　　者：赵文强[1] 丁宣浩[1] 

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《重庆工商大学学报（自然科学版）》2012年第7期9-13,共5页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(10871217);重庆市教委资助项目(KJ110701);重庆市教委科技项目(KJ120703)

摘　　要：泰勒定理是把函数用多项式近似表示的重要依据,是数学分析课程的重要内容.给出了泰勒定理的不同证明,讨论带不同余项的泰勒公式之间的关系,以及在积分计算、级数收敛性判断等方面的应用.Taylor Theorems,which is an important part in mathematical analysis textbooks, present the basis for approximately describing a function by polynomial. In this paper, we give the different proofs about Taylor Theorems and discuss their relationships between Taylor Theorems with different remainders and their applications to such as integral calculation and determination of the convergence of series, etc.

关 键 词：泰勒定理 Lagrange型余项 Peano型余项 积分型余项 柯西型余项 

分 类 号：O172.2[理学—数学]