| 关于求解极限的若干思考 |
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| 引用本文： | 周燕,林丽琼,任立英.关于求解极限的若干思考[J].大学数学,2021,37(2):108-113. |
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| 作者姓名： | 周燕 林丽琼 任立英 |
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| 作者单位： | 福州大学 数学与计算机科学学院,福州 350108 |
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| 基金项目： | 福州大学"三全育人"综合改革精品项目;福建省本科高校教育教学改革研究项目 |
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| 摘 要： | 无穷小等价替换是计算极限一种常用且好用的方法,但要求替换项在极限点的某个邻域内没有零点,文章证明了函数在极限点的任意邻域都出现零点时,满足一定条件,等价替换仍可实施.另外利用极坐标计算二元函数极限时有诸多的限制,文章针对一类特殊函数给出了应用极坐标便于计算应用的若干结论.
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| 关 键 词： | 无穷小 等价替换 极限 极坐标 |
Some Thoughts on Solving Limits |
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| ZHOU Yan,Lin Li-qiong,REN Li-Ying.Some Thoughts on Solving Limits[J].College Mathematics,2021,37(2):108-113. |
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| Authors: | ZHOU Yan Lin Li-qiong REN Li-Ying |
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| Institution: | (College of Mathematics and Computer Science,Fuzhou University,Fuzhou 350108,China) |
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| Abstract: | Infinite equivalent substitution is a common and easy to use method to calculate the limit,but it is required that the substitution term has no zero point in a neighborhood of the limit point.This paper proves that when the function has zero point in any neighborhood of the limit point,it satisfies certain conditions.Equivalent substitution can still be implemented.In addition,there are many limitations in calculating the limit of binary function by polar coordinates.In this paper,some conclusions are given for a special class of functions. |
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| Keywords: | infinitesimal equivalent substitution limit coordinate |
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