| 多元函数在一元微积分中的一些应用 |
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| 引用本文： | 郑平,赵洁,李碧琦.多元函数在一元微积分中的一些应用[J].甘肃高师学报,2013,18(2):117-118. |
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| 作者姓名： | 郑平 赵洁 李碧琦 |
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| 作者单位： | 兰州城市学院数学学院,甘肃兰州,730070 |
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| 摘 要： | 举例说明了如何把多元函数的一些性质应用于解决一元微积分的问题中.如用多元函数的偏导解决一元隐函数的求导问题,用多元函数的拉格朗日乘数法来求一元函数的极值,用二重积分求平面图形的面积,三重积分求旋转体的体积等等.
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| 关 键 词： | 多元函数 一元函数 偏导 面积 体积 |
Application of Multivariable Functions in Single-variable Calculus |
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| ZHENG Ping
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ZHAO Jie
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LI Bi-qi.Application of Multivariable Functions in Single-variable Calculus[J].Journal of Gansu Normal College,2013,18(2):117-118. |
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| Authors: | ZHENG Ping ZHAO Jie LI Bi-qi |
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| Institution: | (Department of Mathematics, Lanzhou City University, Lanzhou Gansu 730070) |
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| Abstract: | This study aimed to investigate the application of properties of multivariable functions for solving single-variable calculus problems. For this paper, we examined the following application problems： calculating the derivative of a single-variable implicit function with the use of the muhivariable function＇s partial derivatives, finding the limit of a single variable function by means of a Lagrange multiplier, using double integrals to find area and evaluating volumes of revolution via triple integrals. |
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| Keywords: | multivariable function single-variable function partial derivative area volume |
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