一道数列极限题的注记

用几何方法分析了高等数学中的一道数列求极限的题目,直观地显示了该数列趋向于极限的方式.并把极限的结果从实数域中拓展到复数域中,指出了该数列在复数域趋向于极限的方式是螺旋的,在实数域中趋向于极限的方式是沿直线靠近的.最后类比该数列,构造出相似数列的求极限问题.     

范希尔理论指导下的数列教学

数列的相关知识是高中数学课程的重点之一,现实生活中的许多问题,例如增长率、银行信贷、环境绿化等都与数列问题有关,此外数列中还涉及到累加、累乘、错位相减等多种计算方法以及递归的思想、极限思想、函数思想、数形结合思想等,这些思想都是初等数学与高等数学重要的衔接点.在历年的高考中可以发现,对数列的考查要求也非常高,除了直接考查数列通项公式和计算数列前n项和之外,还会将数列与函数、不等式、算法程序等问题进行综合考查.因此,如何执教数列问题,值得思考.     

试谈极限的计算

计算数列和函数的极限是数学分析的基本运算之一。计算极限除了要熟练运用四则运算的极限法则以外,还必须掌握和运用一些常用的方法和技巧。 数列极限与函数极限之间有着十分密切的关系。如果存在,则必有:因此,当要计算时,如果有一函数f(x)存在,能使a_n=f(n),则可先算。若这个极限存在,必有,这样数列极限问题通过函数极限计算得到解决。但是,并非任何数列极限问题都能化为函数极限问题。当数列的通项本身呈现n项之     

化归思想在递推数列中求通项的应用

化归思想是指在解决问题的过程中,将那些有待于解决或难以解决的问题转化为已经解决或容易解决的问题的一种数学思想方法.而数列是高中数学的重要内容之一,是初等数学与高等数学的一个重要衔接点;数列的通项公式则是研究数列性质的最佳载体,反映着数列中每一项的共性特征,即通项中包含问题的规律性.     

由高等数学习题教学谈创新能力的培养

结合教学实践,展示在高等数学习题课中,基于一道数列极限题目,尝试"问题-实验-分析-猜想-证明-创新"的教学模式,以培养学生创新意识的过程.     

一个极限问题的两种解法

针对第13届美国普特南数学竞赛的一道数列极限题,将原本不具有单调性质的数列转化为单调数列,并利用单调有界原理及数学归纳法,得出其极限,此方法可推广用以解决同类的一般性数列求极限.此外,此题也可采用不动点原理,简化计算过程.     

数列与上、下极限

一、引言高等数学与初等数学的区别,除了研究对象不同外,主要是研究方法上的不同,而理解极限概念、掌握极限方法,是能否学好数学分析的关键,数列极限的学习又是学习极限理论的重要基础. 关于收敛数列的极限和性质等内容,在各类教材和有关材料中都有较详尽的讨论.这里,将对数列作进一步的讨论,介绍上,下极限的概     

函数极限的局部逆问题

函数极限的计算是高等数学基本运算之一.在计算函数极限的问题中往往遇到这样一类问题,已知函数的极限值,试确定函数表达式中待定常数的值.我们不妨称此类问题为函数极限的局部逆问题.     

10极限导数

10.1 极限 内容概述 1.由于数列的极限在中学数学与高等数学中起着重要的衔接作用,因此这类题目历来是高考常考内容.     

数列的极限,数学归纳法

1　考点简析本单元中的数列极限是中学数学的难点 ,数学归纳法是中学数学中唯一的以专题形式来讲授的推理方法 ,都是今后学习高等数学的基础 ,因此是高考的必考内容 .在高考中所占全卷的比例约1 0 % ,难度一般为中等题 ,也有和不等式综合构成的较难的探索题和应用题 ,目的是为了考查这部分基础知识及应用基础知识解决问题的能力 ,在教学过程中只须把握基本知识 ,适当地掌握一些基本方法 ,重在分析问题 .不要拔高教学高度 ,不随意增加学生学习该部分的难度 .本单元在高考中常考的知识点有 :数列极限的四则运算 ,常用的数列极限值 ,ｌｉｍｎ→…     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Bases of the identities of products of certain varieties of groups

The following theorem is proved: The product of any variety of two-step solvable groups and a variety having a finite basis of identity relations has a finite basis of identity relations.Translated from Matematicheskie Zametki, Vol. 5, No. 1, pp. 137–144, January, 1969.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.