名校
解题方法
1 . 已知a,b,
,且
.
(1)求证:
;
(2)若不等
对一切实数a,b,c恒成立,求x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f306d2b261f4c39a9fc0858d96e647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86fc55969af0c1cf0e9c91e18f5768e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145dfebf6562bc71b46c94883a1b8d3.png)
(2)若不等
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6790cd93c6b394584320dc5d94d96a9.png)
您最近一年使用:0次
2023-02-22更新
|
239次组卷
|
2卷引用:北京市清华大学THUSSAT2023届高三上学期12月诊断性测试数学(理)试题
解题方法
2 . 已知函数
,设函数
的最小值为m.
(1)求m的值;
(2)若实数a,b,c满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ac12e3a97660c2807636c20dd9d020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求m的值;
(2)若实数a,b,c满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6722a5547531bc5df0f8d9bd48e1af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b60663f5358d06d0c909c1c52e2f8cf.png)
您最近一年使用:0次
2020·北京·二模
解题方法
3 . 已知函数
.
(1)若
的解集非空,求实数
的取值范围;
(2)若正数
、
满足
,
为(1)中
可取到的最大值,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe589eca001b0816009c7e1d083a2c7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aaee11552fe4c0863c104364d923359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若正数
![](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/52b6768f57d615696d5e44736edcf1c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580e71f257bca2d1c4ad237d9db9c46a.png)
您最近一年使用:0次
4 . 已知集合
,且
中的元素个数
大于等于5.若集合
中存在四个不同的元素
,使得
,则称集合
是“关联的”,并称集合
是集合
的“关联子集”;若集合
不存在“关联子集”,则称集合
是“独立的”.
分别判断集合
和集合
是“关联的”还是“独立的”?若是“关联的”,写出其所有 的关联子集;
已知集合
是“关联的”,且任取集合
,总存在
的关联子集
,使得
.若
,求证:
是等差数列;
集合
是“独立的”,求证:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10cdcb0e77b3ae3e701c6b51e15e2346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9bf4032eb5a9ba68131b15182aa3491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9859aa908844a32c0e1e069a046727.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918f1c94368c3a41177ff42cfedc0eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e0ad51c5541ec3dcca4a9845f8b7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498f92bf2e605cdbc91973e29b047566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4d89801d24aa43f47d6a366aad0571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1ccce8225324817b0577551956464f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62295c36d2e2174908c2bec0eb5b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8021f4f4c253a00360bf8f9425610e1.png)
您最近一年使用:0次
2020-02-09更新
|
1543次组卷
|
9卷引用:北京市朝阳区中国人民大学朝阳分校2021-2022学年高三上学期开学考数学试题
北京市朝阳区中国人民大学朝阳分校2021-2022学年高三上学期开学考数学试题2020届北京市海淀区高三上学期期中数学试题(已下线)专题02 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)北京市海淀区2021届高三模拟试题(一)北京市清华大学附属中学朝阳学校2021-2022学年高二5月月考数学试题北京市第五十七中学2021-2022学年高二下学期期末考试数学试题北京市第八中学2023届高三上学期12月测试数学试题(已下线)考点47 推理与证明-备战2022年高考数学(文)一轮复习考点帮上海市上海中学2022届高三下学期高考模拟3数学试题
名校
解题方法
5 . 已知
.
(1)当
时,求不等式
的解集;
(2)当
时,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e1cd16253b025efb9869672d420181.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb1dc30d4b297c6d5d0d6d91eab1e3b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ad2c42ea312c8328b4ba4484dbe1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff133c17652425c22f0b367e002797df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440fd119e1131651e93f8abc5091c0e1.png)
您最近一年使用:0次
6 . 设
为正整数,区间
(其中
,
)同时满足下列两个条件:
①对任意
,存在
使得
;
②对任意
,存在
,使得
(其中
).
(Ⅰ)判断
能否等于
或
;(结论不需要证明).
(Ⅱ)求
的最小值;
(Ⅲ)研究
是否存在最大值,若存在,求出
的最大值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c724c6119e3e17b6181178ce7e6baf75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d1fd5262cae918d9c8ef6a1bede788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f84aa794bc075d6139177cd2f59925.png)
①对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbba3561714a2b7b7b675e4c319e4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b375f090c551bb2817fa942edbf9bd05.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165df5a77d87e7c534898e995f162562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbba3561714a2b7b7b675e4c319e4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5de90d938c439d3a9a8e5e1880604f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927a02889cbfc416da88181520058c3a.png)
(Ⅰ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb6b5ca66b71ac5daa42ce59f19f72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432851e0d0b7a2924da29b9cc5ca1706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b3e4ab38102e50c861c13496bd215.png)
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(Ⅲ)研究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2020-05-12更新
|
913次组卷
|
2卷引用:2020届北京市西城区高三诊断性考试(二模)数学试题
名校
解题方法
7 . 设函数
,
.
(1)求不等式
的解集
;
(2)设不等式
的解集为
,当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c0d548b6ae5f492e2a2e576a75e6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7247a1888042e9815d61e778a0d1cc22.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17b382a5cd6655179c0e3c11dc26268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2fcf4e3815881d6024134ced1f2bb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94af2a91d5767a133b06dbc355988de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a009c88f666a1e9b55004d80e2a6be.png)
您最近一年使用:0次
2018-03-23更新
|
363次组卷
|
3卷引用:北京四中2018届高三下学期第二次模拟文科数学试题
名校
8 . 已知
,
,且
.
(1)若
恒成立,求
的取值范围;
(2)证明:
.
![](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/89dc8118d95d6c7bd5b7d38667a498e8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3822e4f4c083b39dcc05bc538daa63dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e19e9385bf9b47eb9f81247c829863.png)
您最近一年使用:0次
2018-03-06更新
|
1257次组卷
|
12卷引用:西北师大附中2018届高三下学期第二次模拟数学(文)试题
西北师大附中2018届高三下学期第二次模拟数学(文)试题广东省深圳市2018届高三第一次调研考试文科数学试题甘肃省张掖市2018届全市高三备考质量检测第三次诊断考试数学(理)试题【全国百强校】河北省武邑中学2018届高三下学期第一次模拟考试数学(文)试题【校级联考】闽粤赣三省十校2019届高三下学期联考数学(理)试题2020届重庆市第一中学高三上学期期末考试数学(理)试题2020届四川省绵阳南山中学高三3月网络考试数学(文)试题陕西省西安地区2020届高三下学期八校联考理科数学试题(B卷)陕西省西安地区2020届高三下学期八校联考文科数学试题(B卷)陕西省西安中学2021届高三下学期第二次模拟考试数学(理)试题(已下线)第58讲 不等式的证明(练) — 2022年高考数学一轮复习讲练测(课标全国版)陕西省西安市高陵区第一中学2021届高三下学期二模理科数学试题