| 未定式含二重变限积分极限的计算方法 |
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| 引用本文： | 杨芮,王玥. 未定式含二重变限积分极限的计算方法[J]. 高等数学研究, 2020, 0(3): 26-29,43 |
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| 作者姓名： | 杨芮 王玥 |
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| 作者单位： | 南京师范大学数学科学学院;中国石油大学（华东）理学院 |
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| 摘 要： | 本文通过一道求极限I=limx→0+∫x0^2du*∫√ux*f(u,v)*dv/1-e^1/4x^4的研究生入学试题的分析探讨,对求未定式含二重变限积分极限问题提出了一个基于泰勒展开公式的“阶分析法”,在原有的两种解法基础之上,补充了一个新解法.在结合应用积分中值定理化简二重变限积分时,得到了求一类未定式含二重变限积分极限问题的命题.最后总结了求解此类极限的四种常见方法.
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| 关 键 词： | 二重变限积分 综合应用 极限运算 |
On the Limit Containing a Double-variable Bound Integral |
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| YANG Rui,WANG. On the Limit Containing a Double-variable Bound Integral[J]. Studies In College Mathematics, 2020, 0(3): 26-29,43 |
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| Authors: | YANG Rui WANG |
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| Affiliation: | (School of Mathematics Science, Nanjing Normal University, Nanjing, Jiangsu, 210023, PRC;College of Science, China University of Petroleum, Qingdao,Shandong, 266000, PRC) |
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| Abstract: | In this paper,a classical limit problem in a postgraduate entrance examination is discussed.A new method called“order analysis”is presented,which is based on the Taylor expansion and is effective for evaluating the limit containing a double-variable bound integral.Four approaches to find such a limit are concluded. |
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| Keywords: | double-variable bound integral comprehensive application limit calculation |
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