| 二元函数极限与一元函数可导关系研究 |
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| 引用本文： | 张丽丽.二元函数极限与一元函数可导关系研究[J].大学数学,2010,26(5). |
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| 作者姓名： | 张丽丽 |
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| 基金项目： | 陕西教育厅专项科研基金项目，陕西省自然科学基金项目 |
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| 摘 要： | 给出了一元函数y=f(x)在x0可导与二元函数f(x)-f(y)/x-y在(x0,x0)处极限存在等价的条件,并通过反例系统地研究了它们之间的关系,指出了文1]的错误.
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| 关 键 词： | 一元函数 导数 二元函数 极限 |
A Study on Relations Between Derivatives of Functions of One Variable and Limits of Functions of Two Variable |
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| ZHANG Li-li.A Study on Relations Between Derivatives of Functions of One Variable and Limits of Functions of Two Variable[J].College Mathematics,2010,26(5). |
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| Authors: | ZHANG Li-li |
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| Abstract: | The paper proposes a condition under which the following statements are equivalent:(1)The function of one variable y=f(x)is derivable at the point x0;(2)The limit of the function of two variablesf(x)-f(y)/x-y at the point(x0,x0)exists.Furthermore,the relations between derivatives of functions of one variable and limits of functions of two variables are studied by the counterexamples,and points out the error in the paper1]. |
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| Keywords: | function of one variable derivative function of two variables limit |
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