名校
1 . 给出集合
对任意
,都有
成立
.
(1)若
,求证:函数
;
(2)由于(1)中函数
既是周期函数又是偶函数,于是张同学猜想了两个结论:
命题甲:集合
中的元素都是周期为6的函数;
命题乙:集合
中的元素都是偶函数;
请对两个命题给出判断,如果正确,请证明;如果不正确,请举反例
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305c81b6a05c983ef0dd04962d546bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b005e1e4b8e41c0028cd464835c464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ca8bdc812627d925f00ed7c145d696.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d6c8ce1327c39675b26deeb0cfa49c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5314a9d2205a2beba0dcffb8fd943b18.png)
(2)由于(1)中函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d6c8ce1327c39675b26deeb0cfa49c.png)
命题甲:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
命题乙:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
请对两个命题给出判断,如果正确,请证明;如果不正确,请举反例
您最近一年使用:0次
2 . (1)设
,
,求证:
;
(2)已知
,
,且
.证明:
或
.
![](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/54d8bf9316bb1dfb0559333ce56b35a6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e131cdd242d56b6dba05ab3363ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8e5b510c343f9d3d626fa1a4b36bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36ffaf917dcebc8719f2ca539a774ec.png)
您最近一年使用:0次
3 .
个有次序的实数
,
,
,
所组成的有序数组
,
,
,
称为一个
维向量,其中
,2,
,
称为该向量的第
个分量.特别地,对一个
维向量
,若
,
,
,称
为
维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在6个两两垂直的6维信号向量.
(3)已知
个两两垂直的2024维信号向量
,
,
,
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5b983949f56bc3137d48e72a393b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e3810cf1eca832ef7487d354e474d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/811ba47ff724fd153378ffe14c1e0b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/713ac1eb0d8cce55d51e62ef4a2b1634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42b3123092bbc1c62e30b0253edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bd9ca5f1ebecf069be3b25efafd29a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6460555341932b6b590af7d74b8f0db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42b3123092bbc1c62e30b0253edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3507f3193277c2f2a5e9d83d25cc9366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b73255f197b518efc343bc9776837e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44cfce6ff54e403e1486244d51395bed.png)
(1)直接写出4个两两垂直的4维信号向量.
(2)证明:不存在6个两两垂直的6维信号向量.
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2024-05-03更新
|
374次组卷
|
3卷引用:上海市进才中学2023-2024学年高一下学期期中数学试题
上海市进才中学2023-2024学年高一下学期期中数学试题重庆市乌江新高考协作体2023-2024学年高一下学期5月期中数学试题(已下线)专题03 高一下期末考前必刷卷01(基础卷)-期末考点大串讲(人教A版2019必修第二册)
名校
解题方法
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb5db93a87981f5b5b94726cb11051f.png)
(1)写出
的单调区间以及在每个单调区间上的单调性(无需证明)
(2)解不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f97a1212828a5aade4637eb80cc09bb.png)
(3)若
满足
,且
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb5db93a87981f5b5b94726cb11051f.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f97a1212828a5aade4637eb80cc09bb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26fc882a7ce3bf689c60850235c7d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475c9073257b3d0760e2c6051a82d592.png)
您最近一年使用:0次
名校
5 . 集合
是由
个正整数组成的集合,如果任意去掉其中一个元素
之后,剩余的所有元素组成的集合都能分为两个交集为空的集合,且这两个集合的所有元素之和相等,就称集合
为“可分集合”.
(1)判断集合
、
是否为“可分集合”(不用说明理由);
(2)求证:五个元素的集合
一定不是“可分集合”;
(3)若集合
是“可分集合”,证明
是奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecf4b08032eee10b91a418ec091773b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c4392f75c09edaec2e70c9eccb2b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38aa0ba6ea6e8f10a2159defda4e67f8.png)
(2)求证:五个元素的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1752a1d13ec6a233405fce4d5af61d8f.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
6 . (1)已知实数
,
满足
,求证:
.
(2)若实数
,
为正数,且满足
,用反证法证明:
和
中至少有一个成立.
![](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/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/838b9f49811c77cbf7d12d3af4a63373.png)
(2)若实数
![](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/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eba1d7973f41f2050afd1759a0e480e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfd31530f4f4d297248c3e39f42d8fb.png)
您最近一年使用:0次
7 . 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)
您最近一年使用:0次
名校
8 . 已知集合
为非空数集,定义
.
(1)若集合
,请证明
,并直接写出集合
;
(2)若
且
,集合
,求
的最小值;
(3)若集合
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1218ca84c0ea386cc4af4a7d25fb7d.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd6edb659be68495364855860dca3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e7fd6bf379008c85f6cf6f85871a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e16289945d1d1c529fb1bfd4d828f413.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ca33894cfd022eb3a57cfde78f06b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3489591aa8bf18d0c4c4363964c234db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77239c98c78a026cc03336edca067ea3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9473a5974fa9c4286f90f6a3637411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1868c8a0db983c9cc2695294fa03b1.png)
您最近一年使用:0次
名校
9 . 设
,函数
.
(1)若
,求证:函数
是奇函数;
(2)若
,请判断函数
的单调性,并用定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e59926e0de6c10c6b791cb14cf61268.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
2023-09-28更新
|
880次组卷
|
7卷引用:上海市松江区华东政法大学附属松江高级中学2022-2023学年高一上学期期末数学试题
上海市松江区华东政法大学附属松江高级中学2022-2023学年高一上学期期末数学试题(已下线)第5章 函数的概念、性质及应用单元复习+热考题型-同步精品课堂(沪教版2020必修第一册)(已下线)模块二 专题4《幂函数、指数与指数函数》单元检测篇 B提升卷(人教A)(已下线)期末真题必刷常考60题(22个考点专练)-【满分全攻略】(沪教版2020必修第一册)(已下线)第6章 幂函数、指数函数和对数函数章末题型归纳总结 (1)-【帮课堂】(苏教版2019必修第一册)(已下线)第06讲:指数运算和指数函数-《考点·题型·难点》期末高效复习 广东省佛山市三水区三水中学2023-2024学年高一上学期第二次统测数学试题
名校
10 . 三角比内容丰富,公式很多.若仔细观察、大胆猜想、科学求证,你也能发现其中的一些奥秘.现有如下两个恒等式:
(1)
;(2)
.
根据以上恒等式,请你猜想出一个一般性的结论并证明.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda84160c36ea80bab0cf253b271b16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52105165d9a478ed469397902da1e3d9.png)
根据以上恒等式,请你猜想出一个一般性的结论并证明.
您最近一年使用:0次