名校
1 . 已知函数
,任取
,定义集合
,点
满足
. 设
分别表示集合
中元素的最大值和最小值,记
,试解答 以下问题:
(1)若函数
,则
___ ;
(2)若函数
,则
的最小正周期为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c31ba2787bc36c28c1a3a54e93432cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752cdf76ae4ff6439f513e8bdf3f60cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9723d753c0d5df723a4308a79e5a876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79410ed94f30c4da60838abfa1f01f6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2b282da990e7bd3f05d4026ef5e394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3215494dccf60336e9f7740d19fcbc57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f26d721b107f8b2bc88f3eb0f42c70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be7b58c2b38144b1891d4840b8047cd.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c64ab61f03db328b8860ff20c6b9b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8798ef183db1c22522f2edefd9ba7930.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c90a21879ef3ff035d9790b24c0a535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0999d7e1264bf85be74b29cd9e34db.png)
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解题方法
2 . 三个相似的圆锥的体积分别为
,
,
,侧面积分别为
,
,
,且
,
,则实数
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3411c87c90bd10bbadd9201630bf45f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e7f090201a6e72fbe8bd6bb55cd2cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1134d7995638f04b3700b7e404b2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-16更新
|
1080次组卷
|
4卷引用:湖南省2024届高三数学新改革适应性训练二(九省联考题型)
湖南省2024届高三数学新改革适应性训练二(九省联考题型)河南省部分重点高中2024届高三普通高等学校招生全国统一考试(期末联考)数学试卷 河南省部分重点高中(青桐鸣)2023-2024学年高三上学期期末大联考数学试题(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点5 面积、体积的范围与最值问题(三)【基础版】
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3 . 已知集合
,
,则
的真子集的个数为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b27a988083e198d61484290fbec80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/214d2791bc2d269fc99c8ca059a2080a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
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4 . 已知
为坐标原点,
,
,
,向量
,动点
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad299e2782c072d27e1c54422cc8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,写出一个
,使得有且只有一个点
同时满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a291e0d0e2f620a15826a1aa3c04bc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e77c9666750eb18917c43a03232d7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad299e2782c072d27e1c54422cc8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e163480714acc9dae5005cac65d217d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11332380fd5a9d83ca2825e7e0d5ef66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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2024-02-27更新
|
1273次组卷
|
2卷引用:湖南省长沙市长郡中学2024届高三一模数学试题
名校
解题方法
5 . 如图是一个球形围墙灯,该灯的底座可以近似看作正四棱台.球形灯与底座刚好相切,切点为正四棱台上底面中心,且球形灯内切于底座四棱台的外接球.若正四棱台的上底面边长为4,下底面边长为2,侧棱长为
,则球形灯半径
与正四棱台外接球半径
的比值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://img.xkw.com/dksih/QBM/2024/2/24/3439881745645568/3442029472153600/STEM/0066b9762966488a85b34c65df195b17.png?resizew=105)
您最近一年使用:0次
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6 . 已知圆锥
的母线长与底面圆的直径均为
.现有一个半径为1的小球在
内可向各个方向自由移动,则圆锥
内壁上(含底面)小球能接触到的区域面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
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2024-02-14更新
|
634次组卷
|
3卷引用:湖南省2024届高三数学新改革提高训练二(九省联考题型)
7 . 甲、乙两位同学进行象棋比赛,采用五局三胜制(当一人赢得三局时,该同学获胜,比赛结束).根据以往比赛成绩,每局比赛中甲获胜的概率都是
,且各局比赛结果相互独立.若甲以
获胜的概率不低于甲以
获胜的概率,则p的取值范围为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84783b6ba0f36789519816101a437f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8652ee8d16f102369e0f4baadb191d15.png)
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8 . 函数
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e50ec2c788ce1f2b21a58fea4a1e201.png)
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2024-02-12更新
|
470次组卷
|
2卷引用:湖南省衡阳市第八中学2024届高三下学期模拟预测数学试题
9 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508935d68f5fbac7cf6d57fff053d2c3.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4134ffb236c8aba6a6d71fb29b3cb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508935d68f5fbac7cf6d57fff053d2c3.png)
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10 . 已知随机变量的分布列如下:
1 | 2 | 3 | |
0.1 | 0.7 | 0.2 |
则数学期望
您最近一年使用:0次