名校
解题方法
1 . 已知
,
,
均为正数
(1)求证:
;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8920a005c0b2e5b9cf0f916d1ce20329.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf43bd907a0590831d324d5eff38ea54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd71a22dc65b28a0e6f8e4b9ee9e3b0.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
,
,
,则
,
,
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e034d58b6454a20df2b0d6026b5b5968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedf2cc8a8d26690b514ae6c00c0158f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61dcf4f92122589d5222c58c2cb25db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
3 . 柯西不等式是数学家柯西(Cauchy)在研究数学分析中的“流数”问题时得到的一个重要不等式,而柯西不等式的二维形式是同学们可以利用向量工具得到的:已知向量
,
,由
得到
,当且仅当
时取等号.现已知
,
,
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2c857eec21dd64ccf0ba530883bb6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bcab0226effeccd2a336c23079bc1be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ec52de4dded0d72469acceca3f1549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1befdda5f9e5055b0d2ae58b1b4b201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab138a74db444886abc7fe18947f7a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90e8d5d7fed033f48270b1ff825fcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f448ab705ce98a0b1ab97863d0cbeda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21bca19afee7ec7105293cbd7e96326a.png)
您最近一年使用:0次
2024-05-15更新
|
640次组卷
|
3卷引用:山西省天一名校2023-2024学年高三下学期联考仿真模拟(二模)数学试题
名校
解题方法
4 . 设
为正数,且
. 证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69582b1a383cda899bfae292812f69d.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c69ec969e81e98cc5051a1817ac866.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538f858f3a28c8faa69cb9463d619671.png)
您最近一年使用:0次
2024-05-13更新
|
286次组卷
|
2卷引用:陕西省西安市第一中学2023-2024学年高三下学期4月月考理科数学试题
名校
解题方法
5 . 已知
,当
时,不等式
成立.
(1)求
的最大值;
(2)设正数
,
的和恰好等于
的最大值,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18822a123bc80412508a309ef5dd7159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16195724ab65f5ed0f378a14051ff5bd.png)
您最近一年使用:0次
解题方法
6 . 已知
.
(1)若
,求b的取值范围;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6d9480b686da380941a1a4e2ee9d93.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ab573d12140a6c3bd663cab95c270a.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b18e8e45c5b91a21978a9f9cfcf1886.png)
您最近一年使用:0次
2024-04-24更新
|
172次组卷
|
2卷引用:四川省雅安市2024届高三下学期4月联考数学(理)试题
名校
7 . 已知函数
,m为
的最小值.
(1)求m的植,
(2)已知实数n,p,q满足
,
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63502808190adaeb97a37a0f4eee1d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求m的植,
(2)已知实数n,p,q满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2400d72b1e3145cb21ba719d8a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3ac83c571110d41a396d12d8eea1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6526e19f5af4425fa017e3d38c42116d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235953c833fc96e4ce88e17051aef93c.png)
您最近一年使用:0次
2024-04-24更新
|
189次组卷
|
2卷引用:陕西省安康市高新中学2024届高三下学期3月月考数学(理)试题
名校
解题方法
8 . 已知函数
.
(1)解不等式
;
(2)记(1)中不等式的解集为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98914a2f34d457acf18e36d3b6eac5f6.png)
中的最大整数值为
,若正实数
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc719705ccfab5c3853b08bbbd4676e9.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4509817be39bef4bcde115996ee39e8.png)
(2)记(1)中不等式的解集为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98914a2f34d457acf18e36d3b6eac5f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e99853dddd205a4d75ace309731ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4427e8bff3b496012c7b5066d7f5ad.png)
您最近一年使用:0次
2024-04-17更新
|
466次组卷
|
2卷引用:宁夏固原市第一中学2024届高三下学期模拟考试文科数学试题(一)
解题方法
9 . 已知函数
.
(1)若
,求不等式
的解集;
(2)若对任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e7504b8b44b0fd789c183d981dae275.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76693f7ef9a4dca9c649153b6d7196e4.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee18d7a40f7a7e0dc85b1bd75bf750c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2749d590bdf00e76a4bbbcab87694659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-04-04更新
|
108次组卷
|
2卷引用:陕西省安康市高新中学2024届高三下学期2月月考数学(文)试题
名校
解题方法
10 . 已知
.
(1)求
的解集;
(2)记
的最小值为
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c00c196c040e330a18551d161627aadc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d30e4faeb8359c0e72f10f01842848c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b73ac9f6c8592e734954588e85a8cec.png)
您最近一年使用:0次
2024-04-03更新
|
288次组卷
|
3卷引用:内蒙古呼和浩特市2024届高三第一次质量数据监测理科数学试卷