| 施笃兹定理及其在离散型变量极限中的应用 |
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| 引用本文： | 王秀琴.施笃兹定理及其在离散型变量极限中的应用[J].东北林业大学学报,1992,20(5):109-117. |
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| 作者姓名： | 王秀琴 |
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| 作者单位： | 东北林业大学 |
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| 摘 要： | 洛比达法则是解决函数未定式极限的有力工具,然而,它仅适用于可导的连续函数,对于离散型变量的极限就无能为力了。而此时,施笃兹定理却显示出其独特的作用。文章对施笃兹定理应用到离散型变量的极限问题,进行了严格的理论证明,并将连续函数的变化率推广到离散型变量的变化率;数列的离散变化率等于数列的增量。于是,施笃兹定理可表述为:在一定的条件下,数列之比的极限,等于离散变化率之比的极限。从而认为施笃兹定理是对于离散型极限未定式的洛比达法则。
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| 关 键 词： | 极限理论 离散函数 导数 |
APPLICATION OF O.STOLZ THEORY IN DISCRETE VARIABLE LIMITATION |
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| Wang Xiuqin.APPLICATION OF O.STOLZ THEORY IN DISCRETE VARIABLE LIMITATION[J].Journal of Northeast Forestry University,1992,20(5):109-117. |
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| Authors: | Wang Xiuqin |
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| Institution: | Northeast Forestry University |
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| Abstract: | For the infinitive limitation of function, Ropeta rule is a forceful tool. However, it does only fit for differentiated contineous function, but not to the limitation of discrete variables. At the same time, O. Stolz theory showes itself a unique action. In this paper, O. Stolz theory applied to the limitation of discrete variables has been proved and using the change rate of contineous fuction generalized to that of discrete variables: the discrete change rate of series equals to the increment of series. Therefore O. Stolz theory can be expressed as follows: under the given conditions, the limitation of ratio between series and series equals that of the ratio between the change rate of discrete and discrete. So that the O.Stolz theory can be seen as if it were the Ropeta rule of the infinitive limitation of discrete. |
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| Keywords: | Limit theory Discrete functions Derivative |
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