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1 . 丹麦数学家琴生(Jensen)是19世纪对数学分析做出卓越贡献的巨人,特别是在函数的凸凹性与不等式方向留下了很多宝贵的成果,设函数
在
上的导函数为
,
在
上的导函数为
,若在
上
恒成立,则称函数
在
上为“凸函数”,已知
在
上为“凸函数”,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f6bfdb24ecf5da863405c2b40936ff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967fc84c0b1cc3b9330f54ab5ce9c4d5.png)
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2017-11-15更新
|
968次组卷
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9卷引用:2020届湖北省宜昌市第二中学高三上学期10月月考数学(文)试题
2020届湖北省宜昌市第二中学高三上学期10月月考数学(文)试题广东省阳春市第一中学2018届高三上学期第三次月考数学(理)试题(已下线)单元测试君2017-2018学年高二文科数学人教版选修1-1(第03章 导数及其应用)【全国校级联考】安徽省肥东县高级中学2019届上学期高三8月调研考试数学(文)试题安徽省定远重点中学2019届高三上学期第二次月考数学(理)试题(已下线)【南昌新东方】江西省南昌市新建二中2020-2021学年高三上学期10月第一次月考数学(理)试题湖南省长沙市宁乡市2018-2019学年高三上学期11月摸底考试理科数学试题四川省广安代市中学校2021-2022学年高三上学期入学考试数学(文)试卷1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(文科)试题(六)
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解题方法
2 . 《几何原本》卷2的几何代数法(用几何方法研究代数问题)成了后世西方数学家处理问题的重要依据,通过这一原理,很多代数公理、定理都能够通过图形实现证明,并称之为“无字证明”.现有如下图形:
是半圆
的直径,点
在半圆周上,
于点
,设
,
,直接通过比较线段
与线段
的长度可以完成的“无字证明”为
![](https://img.xkw.com/dksih/QBM/2017/9/23/1780495389802496/1781681644601344/STEM/22e4a4167e864733946943bb7f971a9b.png?resizew=140)
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2017-09-25更新
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1069次组卷
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5卷引用:湖北省孝感市部分重点学校2019-2020学年高二上学期10月联考数学试题
3 . 设
,称
为
的调和平均数.如图,线段
过⊙O的圆心与圆交于点
,
为圆的切线,
为切点,
于
,
在圆上且
于
.
,
,线段__________ 的长度是
的几何平均值,线段__________ 的长度是
的调和平均值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
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4 . 我国南北朝数学家何承天发明的“调日法”是程序化寻求精确分数来表示数值的算法,其理论依据是:设实数x的不足近似值和过剩近似值分别为
和
(
),则
是
的更为精确的不足近似值或过剩近似值.我们知道
,若令
,则第一次用“调日法”后得
是
的更为精确的过剩近似值,即
,若每次都取最简分数,那么第四次用“调日法”后可得
的近似分数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98908c3834d8a95cadda737a9a1997bb.png)
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