| 关于对数和指数的几个不等式 |
| |
| 引用本文： | 姜华.关于对数和指数的几个不等式[J].数学的实践与认识,2010,40(12). |
| |
| 作者姓名： | 姜华 |
| |
| 摘 要： | 研究了关于对数和指数的两个函数:gα(x)=((ln(1+x))/x)~α及h_β(x)=((e~x-1)/x)~β.得到当x0时,g_α(x)+h_β(x)2及g_α(x)h_β(x)1这两个不等式成立的充分必要条件.
|
| 关 键 词： | 对数 指数 不等式 洛毕达法则 |
On Some Inequalities of Logarithmic and Exponential Functions |
| |
| JIANG Hua.On Some Inequalities of Logarithmic and Exponential Functions[J].Mathematics in Practice and Theory,2010,40(12). |
| |
| Authors: | JIANG Hua |
| |
| Abstract: | This paper studies the two functions g_α(x)=(1n(1+x)/x)~αand h_β(x)=((e~x-1)/x)~β(x>0),and obtains the sufficient and necessary conditions ofα,βsuch that the inequalitiesg~α(x) + h_β(x)>2 and g_α(x)h_β(x)>1 exist. |
| |
| Keywords: | logarithm exponent inequality l'hospital rule |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
