名校
1 . 对
,
表示不超过
的最大整数,如
,
,
,我们把
,
叫做取整函数,也称之为高斯(
)函数,也有数学爱好者形象的称其为“地板函数”.早在十八世纪,人类史上伟大的数学家,哥廷根学派的领袖约翰·卡尔·弗里德里希·高斯(
)最先提及,因此而得名“高斯(
)函数”.在现实生活中,这种“截尾取整”的高斯函数有着广泛的应用,如停车收费、
电子表格,在数学分析中它出现在求导、极限、定积分、级数等等各种问题之中.以下关于“高斯函数”的命题,其中是真命题有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c780149aef1bd77162e85f7f8906a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be209b4634a4169d727f9fac198acce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c2995c0d96854e40fe7bc2d8f5b61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172a58c908317118a9dc10694e28fc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb12a8c429c932646603cdb1b74079ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf7537fd23f7ab98003134107f5c793.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f1a3feca6218955446108ebad0a524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db53ed3af14f332f689979b2e6f6ebae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78234133cb1c3b43caed70005c7c4d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a08814914c19366821849ab81a0b00e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac7f090a0e8228961f05e0a000a3d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db53ed3af14f332f689979b2e6f6ebae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db53ed3af14f332f689979b2e6f6ebae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef78de4f847a4c055624b5e7fa41fb7e.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2022-02-20更新
|
1785次组卷
|
5卷引用:江苏省无锡市天一中学2021-2022学年高一强化班上学期期末数学试题
江苏省无锡市天一中学2021-2022学年高一强化班上学期期末数学试题(已下线)突破4.3 对数 (2)(已下线)突破4.3 对数 (2)(已下线)突破4.3 对数(课时训练)-【新教材优创】突破满分数学之2022-2023学年高一数学重难点突破+课时训练 (人教A版2019必修第一册)第4章 指数概念与对数函数(基础、典型、易错、新文化、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
名校
2 . 设
,集合
,若
个互不相同的非空集合,
同时满足下面两个条件,则称
是集合
的“规范
子集组”
①
;
②对任意的
,要么
,要么
中的一个是另一个的子集.
(1)直接写出集合
的一个“规范
子集组”
(2)若
是集合
的“规范
子集组”,
(ⅰ)求证:
中至多有1个集合对
,满足
且
;
(ⅱ)求
的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be5a005db9e743a9d789747744aa6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9d48660f696fc51b97c89fa55d6f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9d48660f696fc51b97c89fa55d6f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09a1f7758d33c33ff89835af98b3ae9.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530c0a8f2359ae7d2a41fe506e9485d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c593806811df400cc37013b0af9cc0a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434600249ca9e717bfe8631f48654dba.png)
(1)直接写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2837786afdd7b9b8bc37823040d7dd64.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072aa5da2f957e3cd057d346797196c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c93e3391890fc877c761121b68cb927.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072aa5da2f957e3cd057d346797196c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d338d650a72e81e395e8d9f5de34702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c593806811df400cc37013b0af9cc0a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fd1b5191ed514e3573cc11a3dd992.png)
(ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
3 . 设
,记
,若
,
,则称A为
中的一个移位集,
为A的一个移位数.记A中的元素个数为|
.
(1)判断下列集合是否是
中的移位集.若是,求出相对应的移位数.
①
,
②
;
(2)若
中所有满足
的集合A都是移位集,求m的最大值;
(3)对任意满足
的集合A都是
中的移位集,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b8b0bc774a1a88cea41abb4e47e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b938a9b748bf1590ea5a6652669643c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d5fa78bfaa823a1d09ab57208532d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2fc2224e26690053448db851fbcbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4978089eb165d2241a35275396794d06.png)
(1)判断下列集合是否是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a48e81b54f78b96294295542b010dfb.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b89a8282cafe1769891b39ec8c0102.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f255c4c9acc49c187ab5990228480c9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05201ef79a5d5904f492845396fb5470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df91ed9bc04acc7b2edb6b522b953efb.png)
(3)对任意满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500aee7a5f2fa5c8cfc6f55b66546024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2021-10-27更新
|
1040次组卷
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4卷引用:黑龙江省哈尔滨市第三中学2021-2022学年高一上学期第一次验收考试数学试题
黑龙江省哈尔滨市第三中学2021-2022学年高一上学期第一次验收考试数学试题江西省吉安市第三中学2021-2022学年高二10月第一次段考数学(理)试题(已下线)突破1.3集合的基本运算(重难点突破)(已下线)第1章 集合与常用逻辑用语(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)