1 . 已知向量
,其中
是两两不相等的正整数.记
,
,其分量之间满足递推关系
,
,
,
,
.
(1)当
时,直接写出向量
;
(2)证明:不存在
,使得
中
;
(3)证明:存在
,当
时,向量
满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e8a74fa30b2e3d26e572a780f8923e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636995f2a3d0002f8770cf3c4b6fb466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e8f6a7f2aa85688acec8fab018bf6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c932970f95c12bddee59fc04f0c02f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843ff24183004a105ff0c73a1fac6a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe08794bdcc386a700cf75d9bb0a255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7455cd15ac74993fb312181398b4695f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ca738a745d910c37350fd771c6bb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b371d5f06d5bb0bb09f4a18d2247ebf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d6817d33e1286003d29ff178b336ca4.png)
(2)证明:不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf16b1434b6595702815e3e28042da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e8f6a7f2aa85688acec8fab018bf6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77a6635810f385ba10cc174277dfc85.png)
(3)证明:存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7399fcd570d1de4057f2059759d18cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52608aa7220d68349e5bc5659072693a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e8f6a7f2aa85688acec8fab018bf6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3264f1d2a4b2ad9a4435cbd1b34296.png)
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名校
2 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2023-07-17更新
|
550次组卷
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5卷引用:北京市顺义区2022-2023学年高一下学期期末质量监测数学试题
北京市顺义区2022-2023学年高一下学期期末质量监测数学试题重庆市南开中学校2023-2024学年高一上学期开学考试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
3 . 对于向量
,若
,
,
三数互不相等,令向量
,其中
,
,
,
.
(1)当
时,试写出向量
;
(2)证明:对于任意的
,向量
中的三个数
,
,
至多有一个为0;
(3)若
,证明:存在正整数
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681bacf0944746afc82249f50ffb9000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f74901036e0163ee8f9e88e1d952aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08320e6e96f872f1fcf6ad8096ebaa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7accba7c6d73b12592f0874c69339d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843ff24183004a105ff0c73a1fac6a01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe08794bdcc386a700cf75d9bb0a255.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7455cd15ac74993fb312181398b4695f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f7f0bf96b369de82471d9f6b6821b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f8c1951e1335981548165f738e6d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5dba77896ed93d7c27df9d0b2c2154.png)
(2)证明:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61fbe58f038432c468241d2771fb85d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f95e54a9b7c66c97dc6ee6161a25c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f4ddebf0e34a5c3e9232ae66709aa.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3d50b452aca40b6e77c2a37ff5bac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8ae325b1927be368df207ed6051707.png)
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2023-03-28更新
|
719次组卷
|
3卷引用:北京市第二十中学2022-2023学年高一下学期3月月考数学试题
名校
4 . 对于有限数列
,如果
,则称数列
具有性质P.
(1)判断数列
和
是否具有性质
,并说明理由;
(2)求证:若数列
具有性质
,则对任意互不相等的
,有
;
(3)设数列
具有性质
,每一项均为整数,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbda012568d1b987d82212f259c224df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc2ea2a3ad08c9b500689edf05315c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3689290fc990f8750bef9a9c3217206e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2794054d69398d2ab71cd9d10249a820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求证:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ac32d1c1245ecf6b501994a32084fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60051144e33707f6aa51b2fe09925268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb993b6e0950ed30054ab1f5b8939aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3151c7e71673e7e315492cdfa71d3808.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23856dd23f57468e9d82b1df395ae3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60051144e33707f6aa51b2fe09925268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f02970990111c4a3c87a5c8a223990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163d50dd737d0985fdba6d7d22d2ee94.png)
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名校
5 . 已知集合
(
且
),
,且
.若对任意
,
,当
时,存在
,使得
,则称
是
的
元完美子集.
(1)判断下列集合是否是
的3元完美子集,并说明理由;
①
;
②
;
(2)若
是
的3元完美子集,求
的最小值;
(3)若
是
(
且
)的
元完美子集,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/952f1e0ce5bd53a6d5e8bb07ea2da5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/410a811a99d6f15164cdda4597323168.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dd50a4fd2329323aa21597e8ff664b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e676073a8d2acb1678fdc705e33f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11aadf01e5fac133cf390407bfad26b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d169a02afabbe304cf64b355bf71742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49972f77c4c3b89116f02cbaba7f9089.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cc21b9d3aa5f307d9c9d63ffaf68dc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfbdcd7014f79de428c1d5e6525aecf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0604cb71df25c9b90c5d7521d3edd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e8ab57234dfc54a5315381c59c94f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa1ec4e4e5893497849dc70a72e2bfae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717995559c925685dacedc60be48fd03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf7c557b1aadac2ee7012fb1e1ba5f8.png)
您最近一年使用:0次
2022-05-12更新
|
733次组卷
|
4卷引用:北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题
北京师范大学附属中学2021-2022学年高一下学期期中考试数学试题北京市第二中学2022—2023学年高一下学期第六学段阶段性考试数学试题重庆市杨家坪中学2022-2023学年高一上学期10月月考数学试题(已下线)专题16 数列新定义题的解法 微点2 数列新定义题综合训练
6 . 对于正整数
,
,存在唯一一对整数
和
,使得
,
.特别地,当
时,称
能整除
,记作
,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4920c1a7681e10fb6cadc38e97e6c550.png)
(1)存在
,使得
,试求
的值;
(2)求证.不存在这样的函数
:
,使得对任意的整数
,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
(3)若
,
(
指集合
中的元素的个数).且存在
,
,
,则称
为“和谐集”.判断:当
时,集合
中有12个元素并且含有
的任意子集是否都为“和谐集”,并说明理由.
![](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/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc44be06f0c814035e7dfe1d6b8fe64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628504e14b3c2ea172a02484a727bca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0116e1383a146ef6406d514764e87666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8954edf77bd075dfb0c3b97a02c55ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4920c1a7681e10fb6cadc38e97e6c550.png)
(1)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a55fa242ba35478b111f2bbffac589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767992f5013f9e1b4d37e51f884d3640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(2)求证.不存在这样的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c7403a619d584956f21284ddc23fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3830ea6ea58c99a0fc1adadccac0fab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b364ee7c2d8705c4efd99da8184ef4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf34614d82a90cc1e587eaa5e11753e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9195b943cc9f227f6affa59a601cc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b5393742efe51da907dd21e66618bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5556dd86322752a457b3a6ba979c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8954edf77bd075dfb0c3b97a02c55ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caddd958ae597c7a1f8f6a9ee2a3200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-04-09更新
|
211次组卷
|
2卷引用:北京市第五中学2021-2022学年高一3月第一次阶段检测数学试题
7 . 设正整数
,集合
,对于集合
中的任意元素
和
,及实数
,定义:当且仅当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ab98a2bf1135cd989822b0738e11d.png)
时
;
;
.
若
的子集
满足:当且仅当
时,
,则称
为
的完美子集.
(1)当
时,已知集合
,
.分别判断这两个集合是否为
的完美子集,并说明理由;
(2)当
时,已知集合
.若
不是
的完美子集,求
的值;
(3)已知集合
,其中
.若
对任意
都成立,判断
是否一定为
的完美子集.若是,请说明理由;若不是,请给出反例.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645003529ce532c0fb8008542f462aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1dbd4409c152b9d4584dc4987ea1f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e41f01126901d1d41def76204ea6f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ab98a2bf1135cd989822b0738e11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5f736b66000c6c6befe2171d5090bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f22fec5a381ae8aca93d876e54c79de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d81180e86359c33e5cca1d7caa1cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475081154c6beb5b0c79539ae90a97d2.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26b3c852186f8f4e70e3e631a303a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2528fbb6a59ba983d1a70c81b0886484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6baf603fa729de597e4cb0c5096befec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd84e04f63b3b274ab0bd43a3602d208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86edf057f9eade338a48f31cff55a1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0eb383920bb68fa496570c3d34dff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c76d8203805842e9a756aa2b7a453a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146c0af5412c503171a5e8701158352b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92247b24065617e962c85a52086261f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79059a3366ed1b339ba1317ce8a1e7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2021-11-04更新
|
769次组卷
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7卷引用:北京市东直门中学2022-02023学年高一下学期期中考试数学试题
北京市东直门中学2022-02023学年高一下学期期中考试数学试题北京市海淀区2022届高三上学期期中练习数学试题北京市顺义区杨镇第一中学2023届高三上学期10月月考数学试题北京市汇文中学2023届高三上学期期中考试数学试题(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)单元高难问题01集合中的新定义问题-【倍速学习法】(人教A版2019必修第一册)北京市陈经纶中学2023-2024学年高二上学期期中考试数学试卷
解题方法
8 . 三棱柱
中,侧面
底面
,
,
,
,
,
是棱
上的一点,过
的平面与
相交于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/fb9719f5-9880-4928-a72a-1ae4c6459d05.png?resizew=196)
(1)求证:
;
(2)若
是
的中点,求证:平面
平面
;
(3)求证:
与平面
不垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cfb38323095090b0fe5eee70b24210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecf0d955692e3ddacbda6035c70a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ee2744394bfbfbeefbb9550d4706c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/fb9719f5-9880-4928-a72a-1ae4c6459d05.png?resizew=196)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26913705e6c9f6e6844dbe59f8e869fb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610f5493bdd40d7865d53984dfb31f4e.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641d9688e81760c02d0dfc4ba015afb1.png)
您最近一年使用:0次
2021-08-15更新
|
479次组卷
|
4卷引用:北京市延庆区2020-2021学年高一下学期期末考试数学试题
北京市延庆区2020-2021学年高一下学期期末考试数学试题江苏省徐州市沛县2021-2022学年高一下学期第二次学情调研数学试题(已下线)第四章 立体几何解题通法 专题一 反证法 微点3 立体几何中的反证法综合训练【培优版】(已下线)第四章 立体几何解题通法 专题一 反证法 微点2 立体几何中的反证法(二)【培优版】
9 . 对
,定义
.
(1)求
的最小值;
(2)
,有
恒成立,求A的最大值;
(3)求证:不存在
,且m>n,使得
为恒定常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f166b8917034ebc7522d1a160707f6a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7de87e4f04e15189c927b34b2e5afb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b206982b923b94befb9985e51f6499cb.png)
(3)求证:不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c29ca729804f56f23d760ab66b79f68.png)
您最近一年使用:0次
2021-07-19更新
|
536次组卷
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3卷引用:北京市一零一中学2020-2021学年高一下学期期末数学试题
名校
10 . 已知a>0,b>0,a+b>2,有下列4个结论:①ab>1;②a2+b2>2;③
和
中至少有一个数小于1;④
和
中至少有一个小于2,其中,全部正确结论的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c70fcaa661df4fbcad820b439accda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9237dbe3a4f28962ef2870b4e7dab599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb82093f9c1ec3ee4218ae8f8377644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165b2250624fc1f1551d6c38991487d6.png)
您最近一年使用:0次
2020-10-27更新
|
965次组卷
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7卷引用:北京市清华大学附属中学2020-2021学年高一10月考数学试题
北京市清华大学附属中学2020-2021学年高一10月考数学试题湖北省黄石市第二中学2020-2021学年高一上学期11月统测数学试题山东省青岛市市北区青岛第十六中学2020-2021学年高一上学期第一学段模块检测数学试题(已下线)3.2 基本不等式(1)-【帮课堂】(苏教版2019必修第一册)(已下线)2.2.2 间接证明(重点练)-2020-2021学年高二数学(理)十分钟同步课堂专练(人教A版选修2-2)(已下线)2.2.2 间接证明(重点练)-2020-2021学年高二数学(文)十分钟同步课堂专练(人教A版选修1-2)陕西省咸阳市武功县普集高中2021-2022学年高二下学期第一次月考理科数学试题