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| 导数定义公式的一个推广及其应用研究 | |
| 引用本文： | 程万里,刘讲军,刘志红,周永涛,程银行. 导数定义公式的一个推广及其应用研究[J]. 河南教育学院学报(自然科学版), 2011, 20(1): 14-15. DOI: 10.3969/j.issn.1007-0834.2011.01.006 |
| 作者姓名： | 程万里 刘讲军 刘志红 周永涛 程银行 |
| 作者单位： | 1. 郑州交通学院,基础部,河南,郑州,450062 2. 郑州经贸学院,计算机科学系,河南,郑州,450058 3. 中国地质调查局,天津地质矿产研究所,天津,300170 |
| 摘 要： | 将导数在某一点的定义f(x0)=lim(h→0)f(x0+h)-f(x0)/h推广为f(x0)=limf[x0+α(x)]-f[x0+β(x)]/α(x)-β(x)(α(x)→0,β(x)→0),从而简化了有关导数定义一类问题的求解. |
| 关 键 词： | 导数 定义 无穷小 邻域 |
A Promotion and Research on the Application of Derivative Definition Formula |
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| CHENG Wan-li,LIU Jiang-jun,LIU Zhi-hong,ZHOU Yong-tao,CHENG Yin-hang. A Promotion and Research on the Application of Derivative Definition Formula[J]. Journal of Henan Education Institute(Natural Science Edition), 2011, 20(1): 14-15. DOI: 10.3969/j.issn.1007-0834.2011.01.006 | |
| Authors: | CHENG Wan-li LIU Jiang-jun LIU Zhi-hong ZHOU Yong-tao CHENG Yin-hang |
| Affiliation: | 1.Department of Basic Course,Zhengzhou Jiaotong University,Zhengzhou 450062,China;2.Department of Computer Science,Zhengzhou College of Economics and Trade,Zhengzhou 450058,China;3.Tianjin Institute of Geology and Mineral Resources,China Geological Survey,Tianjin 300170,China) |
| Abstract: | A point definition of derivative is promoted from f′(x0)=limh→0f(x0+h)-f(x0)/h to f′(x0)=limf[x0+α(x)]-f[x0+β(x)]/α(x)-β(x)(α(x)→0,β(x)→0).Simplified the solution to the relevant problems of derivative defination. |
| Keywords: | derivatives definition infinitesimal neighborhood |
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