This paper proves a corollary of Lagrange estimation formula. Based on this result, a general solution to the limits of a class of sum sequences is obtained.

研究几类函数与其原函数关于周期性之间的关系,结果表明,连续周期函数其任意一个原函数均可分解为一个连续周期函数与一个线性函数之和;并利用该结论讨论一类不能用洛必达法则求解的函数极限计算问题.

本文探讨了一个含三层复合函数(由两层幂指函数复合而得的)的0/0型不定式极限,除了L'Hospital法则、等价无穷小替换、带Peano余项的泰勒公式等经典方法外,还需结合使用一阶带Lagrange余项的泰勒公式进行求解.

高等数学是高等院校一门重要的公共基础课程,文章分析了农林院校高等数学教学改革的必要性与现状,提出模块化教学改革的思路与做法,以供参考.

“当自变量增量趋向于0时,中间变量增量可能取到0”是多元复合函数求导链式法则证明过程中的主要困难.本文通过补充定义的方法克服该难点,在外层函数可微、内层函数可导这一最弱条件下严格化了证明.

一般高等数学教材里,关于两类具有特殊形式自由项的二阶线性常系数非齐次微分方程,均需通过求解特征根,才能假设出特解形式.文章通过推导,得到了一种无须求解特征根便能得到特解形式的简便方法,这对求解此类方程提供了一定的便利.

本文通过探讨一类双向不等式的共同特征,发现其与凹凸函数的几何特征密切相关,据此给出构造双向不等式的一种方法,并给出若干例子.

本文介绍一个区间折半的定积分公式,可用于求解一些难以计算的定积分以及简化定积分计算.

推广和改进了2017年第十四届“景润杯”数学竞赛第四题的结论,得到了一类特殊和式数列极限的计算公式.

利用分段积分公式和积分不等式证明拉格朗日估和公式,并将其应用在求和式数列极限及无穷级数上.

The Chinese Mathematics Competition not only can help to select the potential outstanding talents with good mathematical quality, but also can promote the teachers' teaching level. Based on the experience of the author in other universities and the author's teaching activity, the significance of the competition is stated, current situation is analyzed and possible measures are provided, in order to provide reference for the related studies.

This article is not conducive to personnel training our public school mathematics curriculum exist for analysis. By optimizing the teaching reform of the public base class curriculum, common math teaching content and other aspects, improve students' mathematical thinking skills, mathematical literacy and the ability to solve practical problems.

This article generalizes a class of simple infinite series and its summation in four forms by using simple calculation of convergent series.

This paper introduces two applications of Lagrange function in the process of teaching college mathematics.One application is to introduce the definitions of eigenvalue and eigenvector,and the other one is to solve the dual problem of an optimal problem.

In this paper,a new proof of Taylor formula is presented.The main idea is to show,by using the Rolle Theorem and the determinant computation technique,that the n-th order derivative of the auxiliary polynomials P(x)corresponding to an n-th order differentiable function f(x)admits certain special value.

Using Taylor expansion, a piecewise-defined function can be expanded as power series of （x-xo） in a neighborhood of x0, one for x〉x0 and the other for x〈x0. By comparing the corresponding Taylor coefficients we can establish criteria for the existence of higher derivatives of the function at x = x0.

A general formula of auxiliary polynomials for proving differential mean value problems was obtained,and the method was generalized.

当积分区域具有某种对称性时,利用函数投诉分解式,可以化简并计算有关多元函数的各种积分.

研究平均值函数φ(x)=1/xintegral from n=0 to x(f(t)dt),利用微积分学的有关概念,得到了它和被积函数具有相同或相似的奇偶性、周期性、单调性、连续性、可导性等性质,并配有应用实例.

借助极限、导数的简单知识,推导罗必达第二法则的推广,并给出应用实例.