1 . 证明下列不等式
(1)已知
,
,
,且
,求证:
.
(2)已知
,
,
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cad3aaeb5b444feb152378278f68863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cc7582a7b091b3f0f5a51325e1d0a1.png)
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解题方法
2 . 设
,
均为正实数.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a964f66da41b8153cfcc6e3f826251.png)
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a964f66da41b8153cfcc6e3f826251.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcb704303d42780e613d63fd0e1eacf.png)
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解题方法
3 . (1)
,其中x,y均为正实数,比较a,b的大小;
(2)证明:已知
,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ff50e53d35f0c88f9ba8b5ba681d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec33f3dd246b2deec64c7c40b9b2d663.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7ff50e53d35f0c88f9ba8b5ba681d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882a6e8f86e28c2382ab50e2c8ab0c0c.png)
您最近一年使用:0次
名校
解题方法
4 . 证明下列不等式:
(1)若
,求证:
;
(2)若
,
,
,求证:
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75e17b53ee815ef4853237102ba053e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e271b6e63206285461a7552d11efd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89dbe5f997bd1b79c750c89ac7c87b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e79fa168ab3bc754a4fdd4deea38246.png)
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解题方法
5 . (1)已知
,设
,
,比较
与
的大小;
(2)证明:已知
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec532f119aff0491334d43cf6b1adf70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1166d36cb26ddb11b666ad0faf6a8b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)证明:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a0aa068c979c53361d049ce49987a8.png)
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解题方法
6 . 证明下列不等式:
(1)已知
,求证:
;
(2)已知
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9656db3a38e6c58dc5ceb291173053a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829e09e0f8adbcb6ca7e8902019729f6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc2bb608dcbe043ded3b74d4a8b5140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d2a05075997525049a368aba1c2b46.png)
您最近一年使用:0次
22-23高一上·全国·课后作业
7 . 证明下列不等式:
(1)已知
,求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fa6068289f4227be182cfb255fffb3.png)
(2)已知
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c03ee0bf584ded03aec6e8ed5331e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8fa6068289f4227be182cfb255fffb3.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917d08bdc240c5ce7b4de86f52daa78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfe0d027c553efeeef4ce0fa17ab157c.png)
您最近一年使用:0次
2023-05-23更新
|
980次组卷
|
8卷引用:专题2.2 等式性质与不等式性质-重难点题型检测-2022-2023学年高一数学举一反三系列(人教A版2019必修第一册)
(已下线)专题2.2 等式性质与不等式性质-重难点题型检测-2022-2023学年高一数学举一反三系列(人教A版2019必修第一册)(已下线)第06讲 等式性质与不等式性质-【暑假自学课】(人教A版2019必修第一册)(已下线)2.1 等式性质与不等式性质(重难点突破)-【冲刺满分】(已下线)专题2.1 等式性质与不等式性质-举一反三系列(已下线)高一上学期第一次月考十五大题型归纳(拔尖篇)-举一反三系列(已下线)单元提升卷02 不等式(已下线)考点6 等式性质与不等式性质 --2024届高考数学考点总动员【练】(已下线)3.1 不等式的基本性质(5大题型)-【题型分类归纳】(苏教版2019必修第一册)
2022高一·全国·专题练习
解题方法
8 . 用比较法证明以下各题:
(1)已知
,
.求证:
.
(2)已知
,
.求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca073cbcb823c28d3434100b59f57c38.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad1dc610c2c010574f0fac671b584bb.png)
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9 . 如果向一杯糖水里加糖,糖水变甜了,这其中蕴含着著名的糖水不等式:
.
(1)证明榶水不等式;
(2)已知
是三角形的三边,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f0d8713246c0c3509ec8c3329c949b.png)
(1)证明榶水不等式;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01721633154e61aa2650bf0b8b10e666.png)
您最近一年使用:0次
2023-09-29更新
|
427次组卷
|
6卷引用:河南省新高中创新联盟TOP二十名校2023-2024学年高一上学期9月调研考试数学试题
河南省新高中创新联盟TOP二十名校2023-2024学年高一上学期9月调研考试数学试题河北省沧州市运东七县联考2023-2024学年高一上学期期中数学试题(已下线)高一上学期期末复习【第二章 一元二次函数、方程和不等式】(拔尖篇)-举一反三系列(已下线)1.3等式性质与不等式性质(高三一轮)【同步课时】基础卷(已下线)专题03 不等式-期中考点大串讲(苏教版2019必修第一册)湖北省鄂州市部分高中教科研协作体2023-2024学年高一上学期11月期中数学试题
10 . 已知函数
的定义域为D,若对任意的实数
,都有
成立(等号当且仅当
时成立),则称函数
是D上的凸函数,并且凸函数具有以下性质:对任意的实数
,都有
(
,
)成立(等号当且仅当
时成立).
(1)判断函数
、
是否为凸函数,并证明你的结论;
(2)若函数
是定义域为R的奇函数,证明:
不是R上的凸函数;
(3)求证:函数
是
上的凸函数,并求
的最大值(其中A、B、C是
的三个内角).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc1bc250c8a6523a1be394ff48d4a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39243f2c10a8291d75d65694b2dec94a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f333263260646c494225db8a7476c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd2179ba09ac27fce32baf170528ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddec2919fb0760a9b54440e581d6f7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73223617c8855826298d435673787a94.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c57e815c01a412466a6aa12d3e883a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128d3060b444b2ee0ef61f2420c5109b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8080fef9bdfa92ae70f3e314eef3e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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