论文部分内容阅读
对于两个正数a和b,有各种各样的平均值概念,常见的有这里所述的几个平均值之间有着重要的关系式:H≤G≤A≤C.(1)众所周知,这个关系式可用多种方法证明.本文首先引述一种关于定义平均值的新方法——Moskovitz方法,然后,再在这个定义下,简单地、一次性地证明关系式(1).这种处理方法,既有利于我们认识诸平均值概念间的内在联系,又为初学微积分的人提供了一个利用微积分知识解决问题的美妙例题.
For the two positive numbers a and b, there are a variety of average values, and there are important relationships between several common averages described here: H ≤ G ≤ A ≤ C. (1) Well-known This relation can be proved in many ways. This article first quotes a new method for defining the average value—the Moskovitz method. Then, under this definition, the relationship (1) is simply proved once and for all. The processing method is not only conducive to the understanding of the internal relations among the average concepts, but also provides a wonderful example for the beginners who use calculus to solve problems.