文档介绍：09 级毕业论文答辩稿辅助函数在数学中的应用学号: 90209112 6 组别: 内容提要高等数学中运用辅助函数就像是在几何中添加辅助线,,,就如同架起一座桥梁,不需要大量的算法就可以得到结果. 因此,学习构造辅助函数对于我们证明、解题是非常有帮助的. 本论文是从证明定理与解题两方面分别来阐述辅助函数的作用,通过本文我们会更好的了解辅助函数在数学中的应用. 关键词: 辅助函数定理证明 Abstract S ummary : The auxiliary function is applied to higher mathematics as adding auxiliary line in geometry. It’s applications of mathematics is very important. Use the conventional method may plicated when we encounter special problems. Then we can construct the auxiliary function like a bridge do not need a lot of algorithm to get the result. Therefore, it is very helpful for us to study the structure of auxiliary function to prove and solve problem. This paper expounds the application of auxiliary function respectively from two aspects of theorem proving and problem solving. Through this paper we will know better in mathematics. K eywords: auxiliary function theorem testify 目录一、绪论............................................................................................................................ 1 二、辅助函数在定理证明中的应用................................................................................ 1 (一)构造辅助证明牛顿-莱布尼兹公式................................................................. 1 (二)构造辅助函数证明泰勒公式........................................................................... 2 (三)构造辅助函数证明拉格朗日中值定理........................................................... 4 三、辅助函数在解题中的应用........................................................................................ 5 (一)构造辅助函数证明恒等式............................................................................... 5 (二)构造辅助函数证明不等式............................................................................... 7 (三)构造辅助函数讨论方程的根........................................................................... 9 (四)构造辅助函数证明中值问题......................................................................... 10 (五)构造辅助函数求极限.................................................................................