论导数的“功绩”

导数的出现,为传统函数问题的求解开辟了新的途径,下面就导数在函数问题中的应用举例分析.一、颠覆了函数单调性传统的判别方法函数单调性的判定传统的方法是利用定义,但遇见较复杂的函数,符号的判断确实异常的烦琐,导数的引入为函数单调性的判断,提供了程序     

Incremental deformation analysis of shell and corrugated diaphragm based on arbitrary configuration

With respect to an arbitrary configuration of a deformed structure, two sets of incremental equations are proposed for the deformation analysis of revolution shells and diaphragms loaded by both lateral pressures and the initial stresses produced in manufacturing. These general equations can be reduced to the simplified Koiter's Reissner-Meissner-Reissner (RMR) equations and the simplified Reissner's equations, when the initial stresses are set to zero. They can also be deduced to the total Lagrange form or the updated Lagrange form, respectively, as the structure is specified as the un-deformed or the former-deformed configurations. These incremental equations can be easily transformed into finite difference forms and solved by common numerical solvers of ordinary differential equations. Some numerical examples are presented to show the applications of the incremental equations to the deep shell of revolution and the corrugated diaphragms used in microelectronical mechanical system (MEMS). The results are in good agreement with those from finite element method (FEM).     

螺旋输送器——均衡螺旋曲面的设计计算

本文对两种均衡螺旋曲面——导程呈线性递增的正圆柱螺旋曲面和曲面宽呈线性递增的等导程螺旋曲面的形成及其规律进行论述,并且导出螺旋曲线的空间轨迹方程,由空间轨迹方程进而推导出螺旋曲面的导线孤长和面积的计算方法。     

新题征展(125)

A 题组新编 1.(1)设数列{an}由a1=5,a2=23,an+2=5an=1-an(nΕN*)确定. ①求证{an+1-5-√21/2an}是等比数列; ②求数列{an}的通项公式. (2)若把无理数(5+√21/2)2011写成小数,求其个位数字及十分位、百分位上的数字.     

妙求值域一例

<正>文[1]用向量知识对三角形的重心的充要条件进行了证明,但在证明充分性时出现了一个常识性错误,特将部分过程摘录如下:     

导数压轴得分少,只因参数在『干扰』

纵览近些年的高考真题,不难发现函数与导数压轴题中总是有参数的参与,这基本上是它的基本特征.学生怕参数,感觉难以驾驭.事实上导数压轴题的解答过程确定让人眼花缭乱,其实含参问题的本质就是分类讨论.教师只需将常见的分类讨论类型一一介绍,并总结解决分类讨论的方法与注意事项,含参问题就能迎难而解了.     

例谈导数法可能引起的错解

导数作为高中数学的新增内容,为解决函数单调性、最值(极值)、零点及交点问题提供了有力的工具.但借助导数工具解决某些特殊函数时还有一些注意的地方,否则会导致一些不易察觉的错误,下面举例说明.