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二元函数求极限的若干方法研究
发表时间：2016-01-15 浏览量：2752 下载量：2255
| 全部作者： | 张付臣 |
| 作者单位： | 重庆工商大学数学与统计学院 |
| 摘 要： | 求二元函数的极限是微积分课程中的重要内容，对于判断二元函数的连续性起着非常重要的作用。研究主要针对求解二元函数的极限计算问题，总结了几种常用的求解方法与技巧——定义法、换元法、等价无穷小量替换法、两边夹准则法、放缩法、有界量与无穷小量的乘积是无穷小量法、利用极坐标代换法等，并给出求解实例。上述解题方法在实际运用中需要相互结合、灵活运用，这有助于满足学生的好奇心和求知欲，使之在生动形象、风趣幽默的课堂情境中，增长见识，提高创新能力，并可大大地激发学生的参与热情和学习兴趣。 |
| 关 键 词： | 数学分析；二元函数；极限；求解方法 |
| Title： | Study on calculation methods of the limit of function of two variables |
| Author： | ZHANG Fuchen |
| Organization： | College of Mathematics and Statistics, Chongqing Technology and Business University |
| Abstract： | The limit of the function of two variables is an important content in the course of calculus calculation. Also, the limit of the function of two variables plays a very important role in the continuity of functions. For beginners, it is difficult to obtain the limit of function of two variables. This paper mainly aims at calculation problem of the limit of the function of two variables, summarizes several commonly used methods and techniques. For example, definition method, substitution method, equivalent infinitesimal replacement method, on both sides of the clip criterion method, scaling, circles and infinitely small quantity of the product is infinitesimal method, using polar coordinate transformation method, etc. These methods are not alone in the practical use, sometimes several methods need to be combined with each other. This is helpful for satisfying students�curiosity and desire for knowledge, making the students study in a vivid and humorous classroom context, enriching their knowledge, improving their innovation ability, and stimulating students�enthusiasm and interest greatly in learning. |
| Key words： | mathematical analysis; function of two variables; limits; calculation method |
| 发表期数： | 2016年1月第1期 |
| 引用格式： | 张付臣. 二元函数求极限的若干方法研究[J]. 中国科技论文在线精品论文，2016，9（1）：71-74. |
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