| 不同形式的泰勒定理及其应用 |
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| 引用本文： | 赵文强,丁宣浩.不同形式的泰勒定理及其应用[J].重庆工商大学学报(自然科学版),2012,29(7):9-13. |
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| 作者姓名： | 赵文强 丁宣浩 |
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| 作者单位： | 重庆工商大学数学与统计学院,重庆,400067 |
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| 基金项目： | 国家自然科学基金，重庆市教委资助项目，重庆市教委科技项目 |
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| 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.
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| 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 |
On Different Types of Taylor Theorems and Their Applications |
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| ZHAO Wen-qiang,DING Xuan-hao.On Different Types of Taylor Theorems and Their Applications[J].Journal of Chongqing Technology and Business University:Natural Science Edition,2012,29(7):9-13. |
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| Authors: | ZHAO Wen-qiang DING Xuan-hao |
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| Institution: | (School of Mathematics and Statistics,Chongqing Technology and Business University, Chongqing 400067,China) |
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| Abstract: | Taylor Theorems,which is an important part in mathematical analysis textbooks,present the basis for approximately descrbing a function by polynomial.Inthis paper,we give the different ptoofs 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. |
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| Keywords: | Taylor Theorem Lagrange type remainder Peano type remainder integration type remainder Cauchy type remainder |
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