| 高等数学中某些问题的探讨 |
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| 引用本文： | 杨华宣.高等数学中某些问题的探讨[J].桂林电子科技大学学报,2004,24(5):72-76. |
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| 作者姓名： | 杨华宣 |
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| 作者单位： | 广西工贸职业技术学院,公共基础部,广西,南宁,530003 |
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| 摘 要： | 高等数学中的函数单调性的导数判定法。比较简单易行地解决了函数单调性的判定问题。但此"判定法"的证明,是基于函数单调性的通常定义(全局性的)之上,借助拉格朗日中值定理才能达到。通过对函数单调性的另一个定义(局布性的)进行了探讨创新,直接利用导数的性质给予证明,将"判定法"撇开拉格朗日中值定理这一铺垫,给人一种更直接了当、行之有效的判定证明。
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| 关 键 词： | 单调性 等价定义 广义积分 收敛反例 |
| 文章编号： | 1001-7437(2004)05-72-05 |
| 修稿时间： | 2004年7月23日 |
A Research on Some Advanced Mathematics Problems |
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| YANG Hua-xuan.A Research on Some Advanced Mathematics Problems[J].Journal of Guilin Institute of Electronic Technology,2004,24(5):72-76. |
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| Authors: | YANG Hua-xuan |
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| Abstract: | In advanced mathematics, the "derivae method for monotonicity judgment of functions" can easily solve the judgment of monotonicity of functions. However, to prove the correctness of this method, it is necessary to resort to the general definition of monotonicity of functions (general) as well as the langrange mean value theorem. The author explores and innovates the other definition of monotonicity of functions (specific). Then, based on the fact that this judgment works without the consideration of langrange mean value theorem, the author directly proves the method regarding the characteristic of functions. The work is not only direct and effective, but also original. |
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| Keywords: | monotonicity equivalent definition improper integral convergence counter example |
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