名校
解题方法
1 . (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/1af972332e5a9149d66e5a2577e71d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2b8f0b94dcf960ca3659536d077d62.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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2022-05-05更新
|
1062次组卷
|
8卷引用:河南省濮阳市油田第二高级中学2021-2022学年高二上学期9月考试文科数学试题
河南省濮阳市油田第二高级中学2021-2022学年高二上学期9月考试文科数学试题广东省广州市铁一三校2022-2023学年高一上学期期中数学试题贵州省兴义市顶效开发区顶兴学校2022-2023学年高一上学期期中考试数学试题内蒙古包头钢铁公司第四中学2022-2023学年高一上学期期中考试数学试题(已下线)3.1 不等式的基本性质 (1)(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)2.1 等式性质与不等式性质练习河南省周口市鹿邑县第二高级中学校2023-2024学年高一上学期第一次月考数学试题
名校
解题方法
2 . (1)已知a,b,x均为正数,且
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3085495517cf7b77cc88e513fa874cc.png)
(2)已知a,b,x均为正数,且
,对真分数
,给出类似上小题的结论,并予以证明
(3)证明:
中,
,(可直接应用第(1)(2)小题的结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3085495517cf7b77cc88e513fa874cc.png)
(2)已知a,b,x均为正数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a89521e1106f61e66c762b5eb66bb1a3.png)
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名校
3 . 已知函数
.
(1)求函数
的极值;
(2)设函数
有两个极值点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86d97d22525157c58a5148cdbf51a2c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e38e9aa7ea6401f10eae6ef9a6a45c6.png)
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2024-03-03更新
|
348次组卷
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4卷引用:第五章综合 第二练 数学思想训练
(已下线)第五章综合 第二练 数学思想训练(已下线)专题07 函数的极值和最值的应用8种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)吉林省长春市实验中学2023-2024学年高二下学期5月期中考试数学试题安徽省六安市2024届高三上学期期末教学质量检测数学试题
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4 . 基本不等式是高中数学的重要内容之一,我们可以应用其解决数学中的最值问题.
(1)已知
,
R,证明
;
(2)已知
,
,
,
R,证明
,并指出等号成立的条件;
(3)已知
,
,
,
,证明:
,并指出等号成立的条件.
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
,证明:
;
②已知
,
,且
,求
的最小值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1f5facca1d0db44613d7c690bc90aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267cd7062303bbe8d8a4bd8dd48fef2e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7701d084d2b153bbea08cfbf63413a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61d582437402db050313612348dfa27.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d51126fd77ba262607809563550b48f.png)
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5acd1467c10c7ff14caca53feea7a540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d49468bf449d201b533f5f8f9e9add1.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983154ee44321cef8eb8213bd862c70d.png)
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2024-02-10更新
|
141次组卷
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2卷引用:河北省邯郸市永年区第二中学2023-2024学年高二下学期6月月考数学试卷
5 . 正项数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dcdd36191a256bc058ada311209fb3.png)
(1)求数列
的通项公式;
(2)
,
时,
①证明:
;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dcdd36191a256bc058ada311209fb3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c404d276cdabdb544091df37f3cfb292.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242a27a7a522c6461753218cac3d0066.png)
您最近一年使用:0次
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6 . 设
是等差数列,
是等比数列,且
.
(1)求
与
的通项公式;
(2)设
的前
项和为
,求证:
;
(3)若
,且数列
的前
项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6eba282321f5d17e3de9b6544e9f6f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702b31070b4001b47426d73831e585b5.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc79e006b192782170fdb16384ba5879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0022c073e919d163032a4f5923e893ef.png)
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7 . 已知
与
都是定义在
上的函数,若对任意
,
,当
时,都有
,则称
是
的一个“控制函数”.
(1)判断
是否为函数
的一个控制函数,并说明理由;
(2)设
的导数为
,
,求证:关于
的方程
在区间
上有实数解;
(3)设
,函数
是否存在控制函数?若存在,请求出
的所有控制函数;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7493c0fcdc634aa03efb6be277e23769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f937c7606a3ab00e17e34b39144a0ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac42f0a061cd4fe9db72f8717a5ab173.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e14206c7d228a7c2259a7b27da8813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7a9a783d62f5967e662a562211e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7ed99a74e126a05cb520f19c094020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
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8 . 已知
为等差数列,
为等比数列,
.
(1)求
和
的通项公式;
(2)设
,求数列的前
项和
.
(3)设
,求数列
的前
项和
.
(4)记
的前
项和为
,求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0073e3d5e02310aa42b531a8436f88.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d44ddab6e0c60119be69985ae7fa65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15526f7c892333030073b85fc3baee6.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d53fb7fa268af00a904751bba9cefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(4)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0664a5e5167818da722b370b4409ce1.png)
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2023高一·全国·专题练习
解题方法
9 . 已知b g糖水中有a g糖
,往糖水中加入m g糖
,(假设全部溶解)糖水更甜了.
(1)请将这个事实表示为一个不等式
(2)证明这个不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b37253262ce9d07748ed45a55156e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344cc24b575f4fd1ea7fe8ce5612fa9a.png)
(1)请将这个事实表示为一个不等式
(2)证明这个不等式
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解题方法
10 . 求解或证明下列各组中两个代数式的大小:
(1)已知
均为正实数,比较
与
﹔
(2)已知
,证明:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2b05214c8b22507f0c36b110593d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a977414a3ad65caf5eee28e0cd175de.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e8fee0c9fe95497e8c093c8e43d8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c983849aee8e09ac232bdf28f4cfdf3.png)
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2023-07-26更新
|
602次组卷
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2卷引用:宁夏中卫市中宁县第一中学2022-2023学年高二上学期10月月考数学试题