再证一个组合等式

文[1]和文[2]都用不同的方法证明了以下等式：     

关注公式使用条件

<正>问题已知函数f(x)=ln(2+3x)-3/2x2,若对任意x∈[1/6,1/3],不等式|a-lnx|+ln[f′(x)+3x]>0恒成立,求a的取范围.周老师在《由错误引发的再思考》(中学生数学,2014,1(上))(文(*))中提到了两种错误的解法,其中一种是将不等式|a-lnx|+ln[f′(x)+3x]>0转化为|a-lnx|>     

小变换 大作用

苏教版教材选修4—2介绍了关于伸压变换的知识,其中介绍了沿着T轴或Y轴方向的垂直伸压,变换,     

解题后的追问

解决一道题目之后的反思与追问,往往能带来一些意想不到的收获,本文呈现解决一道典型题目的追问所得,以飨读者．     

一公式的另证及应用

大家知道,cosθ—cosθ1cosθ2,俗称三余弦公式,对其详细表述是：     

一个推广结论的纠正及思考

题目设x,y,z∈[0,1],则M=√｜x-y｜＋√｜y-z｜＋√｜z-x｜的最大值是：__．     

What is The Squeeze （or Sandwich） Theorem？

Let＇s do an exercise as warming up.Ex：Find lim x→0sin1/x.lim x→0sin1/x=lim1/x→∞sin1/x=lim t→∞sint（Let t=1/x）.We know lim t→∞sint does not exist,so lim x→0sin1/x DNE.We can use graphing calculator to show the result is DNE（from figure 1to figure 8）.     

What does Part 2 of the Fundamental Theorem of Calculus mean?

We defined the indefinite integral as an anti-derivative,and defined the definite integral as the limit of Riemann sums.Both of them are very different and seem to be little in common.Part 1of the Fundamental Theorem of Calculus shows how indefinite integration and definite integration are related.In the other words,it shows how anti-derivative and the area are related.Today,we’ll learn Part 2 of the Fundamental Theorem of Calculus.     

What is the limit of an infinite sequence？

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The definite integral

1. What does the definite integral mean？
The definite integral off（x） from a to b is defined the limit of the sum as n→∞.     

What is the differential equation？

An equation involving a derivative is called a differential equation.Such as,dy/dx=2x,and the function y=f（x）satisfies this equation.When we know the additional condition that y=2 when x=-1,the function y=f（x）will be find exactly.The additional condition is called the initial condition.It is used to evaluate constant of integration.     

Approximation integration by using rectangles

In calculus,two famous problems are well known.The one problem of finding the tangent line led us to the derivative.The other problem of finding area led us to find the definite integral.In this paper,we will learn how to approximation integration by using rectangles.1.What does the Riemann sum mean？A given function y=f（x）is continuous on the interval[a,b].     

The volume of a solid of revolution in calculus

On the last time, you have known what a right circular cylinder is in calculus. Right cir- cular cylinders are just a part of solids of revo- lution. Today you will learn solids of revolu- tion aren＇t right circular cylinders.     

一道全国初中数学竞赛试题的简明解法

李佳蓬同学在本文中给出的解法,确实简明.但读者更希望知道这个巧妙的解法是怎样想出来的,其中有哪些规律性的东西,即对今后解题有帮助的东西.对这些,作者未作说明,只能靠读者自己去思考和体会了.     

特例探路 退中求进——一类探究题的思维策略

苏谆教授曾说:"简单情形正象是一把钥匙、一面镜子,可以为我们解答复杂的数学问题提供启示与借鉴."对于一类以探究"定值"、"定点"、"定线(向)"为特征的数学题,可以通过"主动寻求与建构特例",巧妙锁定思维思维方向,迅速实现问题解决.今以2011年中考题为例作析,仅供读者探究之用.     

Use the Definite Integral to Calculate the Volume of Vase

<正>When I studied at primary school,I learned the ways to calculate the surface area and the volume of rectangle,square and cylinder,and the volume of cone.I kn...