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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。 |
| 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 |
| DOI： |
| 分类号: |
| 基金项目: |
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| On Different Types of Taylor Theorems and Their Applications |
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ZHAO Wen-qiang,DING Xuan-hao
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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. |
| Key words: Taylor Theorem Lagrange type remainder Peano type remainder integration type remainder Cauchy type remainder |
