1 . 已知点集
满足
,
,
.对于任意点集
,若其非空子集A,B满足
,
,则称集合对
为
的一个优划分.对任意点集
及其优划分
,记A中所有点的横坐标之和为
,B中所有点的纵坐标之和为
.
(1)写出
的一个优划分
,使其满足
;
(2)对于任意点集
,求证:存在
的一个优划分
,满足
;
(3)对于任意点集
,求证:存在
的一个优划分
,满足
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d82ea5bd5d061a16d0ba32daacb6dece.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efaead32620574f09623dff495df983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de122ae929b1acaff321dec137622ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9610877bf323ad7e27b83e886220f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc0f5296284e2f6dcba4dbb77b0e141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12cb68674b3cdaeda8b7123c747460fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a47112c5ff4179fca6e28aa4d0d47d21.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b65432b8fcd588460df55bb8a21f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673bf8d12ff9956f1fe4b31d32c201fd.png)
(2)对于任意点集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd919250fa4a36bc880e8038cbc90b.png)
(3)对于任意点集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95d247ffb2774bb7e22708b25daf7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883f136eeb68b72dc768c697ae31e535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9505c141fd8b7c6b4139667bb5853648.png)
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2 . 已知
为有穷整数数列,若
满足:
,其中
,
是两个给定的不同非零整数,且
,则称
具有性质
.
(1)若
,
,那么是否存在具有性质
的
?若存在,写出一个这样的
;若不存在,请说明理由;
(2)若
,
,且
具有性质
,求证:
中必有两项相同;
(3)若
,求证:存在正整数
,使得对任意具有性质
的
,都有
中任意两项均不相同.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0f8b01eee1e48eb49952a1cd678434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87310fb03b3907462f395b1cf2fa9e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1bd1147d3076ee020d6af6c4cc3eaa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8839dbcce0e0b2d56c870075136fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8839dbcce0e0b2d56c870075136fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d9b6c86435e0ceff94d8ad1cd03737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249b92e30f3808f5287db70a9eec6a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09d8084c6590784775495f12d5e8e81.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b70d4a3fc3e01b5a6358cf4e57578e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e713ad45b7234c5aba67f15f5a1f211.png)
您最近一年使用:0次
3 . 定义两个
维向量
,
的数量积
,
,记
为
的第k个分量(
且
).如三维向量
,其中
的第2分量
.若由
维向量组成的集合A满足以下三个条件:①集合中含有n个n维向量作为元素;②集合中每个元素的所有分量取0或1;③集合中任意两个元素
,
,满足
(T为常数)且
.则称A为T的完美n维向量集.
(1)求2的完美3维向量集;
(2)判断是否存在完美4维向量集,并说明理由;
(3)若存在A为T的完美n维向量集,求证:A的所有元素的第k分量和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3e014b5001732bc4b37be2b03c4033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f00efefb7f52ad5c9dbdb180e577ee54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028076d0553b70f0fdae6beff69a10ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c5d928c389d3abb01ca33fedf17efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00da2c261a6ecd7533ffb8e153eaa506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d9e604bcc449034230149a89d746a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b4b3879d1c6debf0333008f686634e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea687406a05d37d0761cd1a3455c804f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ba4a7e65c27fb359ba7aadd49f797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d344174267f996c7cefecfd6985d380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cbe607b41f76db6418ce01831a1d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d9e604bcc449034230149a89d746a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fdb50eea11f40d9f3c37052c45894a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57aabc9b21bc15ae35720679a7b6d1ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10772b376bc43eb5c33cfd7ba9771657.png)
(1)求2的完美3维向量集;
(2)判断是否存在完美4维向量集,并说明理由;
(3)若存在A为T的完美n维向量集,求证:A的所有元素的第k分量和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912092af5b5301c659e6e86a7e858f38.png)
您最近一年使用:0次
2024-04-23更新
|
659次组卷
|
2卷引用:2024届江西省九江市二模数学试题
4 . 已知集合
,对于
,
,定义
与
之间的距离为
.
(1)已知
,写出所有的
,使得
;
(2)已知
,若
,并且
,求
的最大值;
(3)设集合
,
中有
个元素,若
中任意两个元素间的距离的最小值为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46717c433c9f34b936f694eba762ccb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0135cb7ffda469b422df0aa1817d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c76f1774902da4c8da18791b5a35c65.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/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3231e2c7d20174642764c2a96427636d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c72cbaca91d8e578762c4f0b6750a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e79b6edfd5f5bb3866599fcb2aa6f3.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea7b72192ddc13754ebc4c3d70b40ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e77ba8c90d21237670483bbcd8ac63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b9dbb9c52862ac974003241d68fb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2b280a6a65c9bf2f20cad5d1106080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2ea5126ca30d68cc8b70f03860ba2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d528f49ab8d7fd971c5bb8fa7f24d4.png)
您最近一年使用:0次
名校
5 . 已知
是各项均为正整数的无穷递增数列,对于
,定义集合
,设
为集合
中的元素个数,若
时,规定
.
(1)若
,写出
及
的值;
(2)若数列
是等差数列,求数列
的通项公式;
(3)设集合
,求证:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/542b4acf7b25b750fbe7205fd179b978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857369257ea1b23ef40ce7e3a0f058af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1202d58cd3ad66e7b23f01024566705b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc57d8a4f67a040435d8b206d3254bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6510d0816033afa001c130342bb7cda.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b6f99a33b14f53fb398a195aa2ec3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac648580405ecaa29e91d45738a08af7.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b54e4701d4cb8d0133ad2044a7e0f52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1479e28bf6a8cb64ec7df77cd295f99d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30a6a3d1be93cf6d16ee6e0ce0497f46.png)
您最近一年使用:0次
2024-01-21更新
|
1357次组卷
|
7卷引用:广东省江门市开平市忠源纪念中学2024届高三下学期高考冲刺考试(一)数学试卷
广东省江门市开平市忠源纪念中学2024届高三下学期高考冲刺考试(一)数学试卷江苏省常州市华罗庚中学2024届高三下学期4月二模训练数学试卷北京市朝阳区2024届高三上学期期末数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)讲(已下线)2024年高考数学二轮复习测试卷(北京专用)(已下线)黄金卷01(2024新题型)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编
名校
6 . 如果
同时满足以下三个条件:
①
;②对任意
,
成立;③当
,
,
时,总有
成立,则称
为“理想函数”.有下列两个命题:
命题
:若
为“理想函数”,则存在
且
,使
成立;
命题
:若
为“理想函数”,则对任意
,都有
成立.
则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf2489be061d0834df02c319a798e33.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12aae852c3129efc16934aefc54201f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cd2fe62ffe3caa1c6f7976851c9dc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2f51cd760aeff9365b51e9a85b41e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f6988640a0b9bc4f9637132e6ca470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6c0fddb9074dfc96be03b4aa24d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d3c756a52c9185ae6d02d9b9312f29.png)
则下列说法正确的是( )
A.命题![]() ![]() | B.命题![]() ![]() |
C.命题![]() ![]() | D.命题![]() ![]() |
您最近一年使用:0次
2023-11-13更新
|
303次组卷
|
3卷引用:上海市光明中学2023-2024学年高三下学期三模数学试题
名校
解题方法
7 . 已知数列
满足
.给出以下两个命题:命题
对任意
,都有
;命题
,使得对
成立.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ffc57aa0b1ddf28ff0f3cf60046bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51441c8788ff11be766766227793246d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc6729ce5acf495ef7bc801212383ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a144ed624f56d67e36c99e5439a12d77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7217e6677b7fb5cbfc50a33c5ae6dcba.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 上海入夏的标准为:立夏之后,连续五天日平均气温不低于22℃.立夏之后,测得连续五天的平均气温数据满足如下条件,其中能断定上海入夏的是( )
A.总体均值为25℃,中位数为23℃ |
B.总体均值为25℃,总体方差大于0℃ |
C.总体中位数为23℃,众数为25℃ |
D.总体均值为25℃,总体方差为1℃ |
您最近一年使用:0次
9 . 设函数
.
(1)设
,求函数
的单调区间;
(2)求证:
是
有三个不同零点的必要而不充分条件;
(3)设
,
,
,证明:函数
恰有一个零点r,且存在唯一的严格递增正整数数列
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae06c488100e31570805778b1d322e4.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d3469fb79917724365db2b2829d512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0c84cafbf166a261fa4dbf66df8c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baddffb31adacf907742ca666e32d664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ea0e903fbb4c8ce04133b9969578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba5fb2a39d08006bf9dd4bb689d0f4c.png)
您最近一年使用:0次
10 . 已知数列
的前
项和为
,对任意的正整数
,点
均在函数
图象上.
(1)证明:数列
是等比数列;
(2)问
中是否存在不同的三项能构成等差数列?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3768db0f2e2881b810d44ddc39ff295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e89b5a13cba4ed604340409c11df75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(2)问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次