名校
解题方法
1 . 在
中,
对应的边分别为
.
(1)求
;
(2)奥古斯丁•路易斯・柯西,法国著名数学家.柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.
①用向量证明二维柯西不等式:
;
②已知三维分式型柯西不等式:
,当且仅当
时等号成立.若
是
内一点,过
作
的垂线,垂足分别为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c1e84aaa7e1b5c1283075b36c72fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb55ae794081fa9e39ea5657fa5d41e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)奥古斯丁•路易斯・柯西,法国著名数学家.柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.
①用向量证明二维柯西不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1befdda5f9e5055b0d2ae58b1b4b201.png)
②已知三维分式型柯西不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1358300202bcbca3c7a48fa40217a4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5ba135022def1bcc1cddea66496706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e0e66571238a7e1c756b99b3113d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0e08a39c6619123557148d195abfbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d731994627d9911585d053afc821e7.png)
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2024-05-12更新
|
463次组卷
|
5卷引用:山东省实验中学2023-2024学年高一下学期4月期中考试数学试题
山东省实验中学2023-2024学年高一下学期4月期中考试数学试题(已下线)【江苏专用】高一下学期期末模拟测试A卷(已下线)专题05 解三角形(2)-期末考点大串讲(人教B版2019必修第四册)山东省青岛市即墨区第一中学2023-2024学年高一下学期第二次月考数学试题广东省广州市真光中学2023-2023学年高一下学期月考数学试题
解题方法
2 . 已知下列五个函数
,从中选出两个函数分别记为
和
,若
的图象如图所示,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0908ff4409d87277ab3b8583837bd1e.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae6be1c40cb864c38df5dcebf5f2035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870a586e90a7bb79dc44f9451dee19ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0908ff4409d87277ab3b8583837bd1e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/5f92437d-7854-4769-a256-899f9ed1c297.png?resizew=116)
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2024-03-07更新
|
169次组卷
|
3卷引用:北京市朝阳区2022-2023学年高一上学期数学期末试题
名校
3 . 已知函数
是定义在
上的奇函数,当
时,
,其中a,m为实数,且
.
(1)当
时,求实数
;
(2)若对任意
,
恒成立,求实数
的取值范围;
(3)试求满足
的所有的实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ca8dbdfa95e4175fcfa2e93336598e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c857db5d3e377851c4a50e2360c8d90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)试求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faf12330c0f061bedad62b8553c902dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
4 . 已知数列
满足:
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7743378bbbd5066278db35f1a5710400.png)
A.若数列![]() ![]() | B.存在![]() ![]() |
C.任意![]() ![]() | D.任意![]() ![]() |
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2024-01-25更新
|
586次组卷
|
4卷引用:安徽省芜湖市2023-2024学年高二上学期1月期末教学质量监控数学试题
解题方法
5 . 已知函数
,其中
.
(1)当
时,若
,求
的值;
(2)证明:
;
(3)若函数
的最大值为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f40b7076417a2d9a77657020cd3d0d1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fadd2e6f0aa16c2c466c904474ffc79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9920ba41061fb4971be07bda1ddfb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0698b324aad6962f9f50b240cffe48.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3125c342e7fcc6ba0aff633dbaf8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 已知定义在
的严格增函数
与
.若对任意实数
,存在实数
和
,不等式
恒成立,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa311daf7a73f8c45de4462f9d92b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302cf658af80ec14f1828b3727e7a511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8578c6d7d390a36d1728070bbd9cc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365114c53aa12abda1004c8e4cb4ca0c.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/c1eb1ef0bb8706a483144babfc03a655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-01-13更新
|
358次组卷
|
3卷引用:上海市五爱高级中学2023-2024学年高一上学期期末考试数学试卷
名校
解题方法
7 . 已知定义在R上的函数
,且
为偶函数.
(1)解不等式
;
(2)设函数
,命题
,使
成立.是否存在实数
,使命题
为真命题?如果存在,求出实数
的取值范围;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd5e6cad472bfe062b2fa44825ba7a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94cc25a7cf28ed096549fbae97fce40a.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea75c146df483a2b7b028b4a4ffb3f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b6183a441fd232d2e6ced6c30aeb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00284ef8927a250233cac770fd09006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 如果函数
满足:对于任意
,均有
(m为正整数)成立,则称函数在D上具有“m级”性质.
(1)分别判断函数
,
,是否在R上具有“1级”性质,并说明理由;
(2)设函数
在R具有“m级”性质,对任意的实数a,证明函数
具有“m级”性质;
(3)若函数
在区间
以及区间
(
)上都具有“1级”性质,求证:该函数在区间
上具有“1级”性质.
![](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/079957ae49da067d35085e6ce81ff8f3.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0089d9b39592e2eef4c486c5055648d7.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e682f89425146ac9cb16b2f13a014c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3819123c00dd8547948fd6a142d23eb8.png)
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解题方法
9 . 设
,
,若函数
在
上的最大值为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0cb5b97e882f20b83c58efbd7de2a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac1e259015a39c6a002506885a47ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
名校
解题方法
10 . 对于空间向量
,定义
,其中
表示x,y,z这三个数的最大值.
(1)已知
,
.
①直接写出
和
(用含
的式子表示);
②当
,写出
的最小值及此时
的值;
(2)设
,
,求证:
;
(3)在空间直角坐标系
中,
,
,
,点Q是
内部的动点,直接写出
的最小值(无需解答过程).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b303ef66609858e8ab234b6dabccba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e382f70d741ee01c165391ce980155d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4461408813c1476a8a8073c83b8989.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23056c429159c0198f865ff11972d8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e17d2355419564f6d9737295412b58c.png)
①直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9873960d64934875139754efbdfe951d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af5f843689a63bc176c2d2171b6a1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53168695826b0a33a23067b76173c7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780ef5119f58f853ce9dd2b9176ffdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778ae4468d857c229073875e0ee0ce31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6772fa3937b97d9ec3aec1ea2ea143b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95086cc97ef93f5166489b3bc47e1911.png)
(3)在空间直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32ab04dd852329d5918b177c199eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee736aec4313d04a5921ed7e5800b3b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d04a00e46c1ffb335f73506041c66dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084fc7655647b596d07e80269d086e5a.png)
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