| 关于1~∞型幂指函数极限的快捷方法 |
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| 引用本文： | 程裕强.关于1~∞型幂指函数极限的快捷方法[J].阜阳师范学院学报(自然科学版),2013,30(2):15-17. |
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| 作者姓名： | 程裕强 |
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| 作者单位： | 玉林师范学院数学与信息科学学院,广西玉林,537000 |
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| 基金项目： | 玉林师范学院应用型专业实践教学改革项目 |
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| 摘 要： | 幂指函数的极限问题是微分学常见问题。由于幂指函数的特殊结构,不定型的幂指函数极限的求解过程显得复杂。针对于1∞不定型幂指函数极限问题,文章给出3种快捷的计算方法。首先给出极限e公式的推广公式,可以快速解决(1+0)∞型幂指函数极限问题;再对一些1∞型极限给出一般求解公式;最后给出幂指函数的等价无穷小替换公式,可以快速化简幂指函数极限求解过程。
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| 关 键 词： | 幂指函数 极限 等价无穷小 |
Fast ways to calculate the 1∞ power-exponential function limit |
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| CHENG Yu-qiang.Fast ways to calculate the 1∞ power-exponential function limit[J].Journal of Fuyang Teachers College:Natural Science,2013,30(2):15-17. |
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| Authors: | CHENG Yu-qiang |
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| Institution: | CHENG Yu-qiang (School of Mathematics ＆ Information Science, Yulin Normal University, Yulin Guangxi 537000, China) |
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| Abstract: | The limit of power-exponential function is common in differential and integral calculus. Due to its special structure,the calculation of the indefinite form of power-exponential function limit seems complicated. For the problem ofthe 1 ^∞ indefinite form of the limit, this paper provides three fast calculation methods. An Extension of e formula limit is first given and it can quickly resolve （ 1 ＋ 0）^∞ problem. Then other fast calculation methods are provided to solve 1 ^∞ problem. Finally, equivalent infinitesimal replacement formula is given, and it can simplify the calculations of power exponential function limit. |
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| Keywords: | power-exponential function limit equivalent infinitesimal |
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