名校
1 . 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
|
1360次组卷
|
7卷引用:北京市朝阳区2024届高三上学期期末数学试题
北京市朝阳区2024届高三上学期期末数学试题(已下线)2024年高考数学二轮复习测试卷(北京专用)(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)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
2 . 中国传统数学中开方运算暗含着迭代法,清代数学家夏鸾翔在其著作《少广缒凿》中用迭代法给出一个“开平方捷术”,用符号表示为:已知正实数
,取一正数
作为
的第一个近似值,定义
,则
是
的一列近似值.当
时,给出下列四个结论:①
;②
;③
,
;④
,
.其中所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55dde645fdd5795b4194e50d6885bf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e40ebe5a203db35552e27bf3f079f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da18ad56af5e38b1a5b73f44ba198fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55dde645fdd5795b4194e50d6885bf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede0f7cac4530e0ed4799a8192283888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835faec9f80596430d7352dcacde9589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c3401c74f3b70fd95a069b6abcf717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3febfa17c874de45558534cc8bbe8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e377f675489078f2fec21a6b5cce0c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c68b253787b7980d259a243ee42ecfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad46a14425d9c75b82b4e1342c57949e.png)
您最近一年使用:0次
名校
解题方法
3 . 在
中,
,当
时,
的最小值为
.若
,
,其中
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11dd0962a6f2e996b1c523783c98acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8d8b400f041ac4a256e1108cd459c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d788a8f1a85eda30184e507bb7bd47bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b845f89bcb2c14dfe441644f499b09e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4206c284be2d1a6aebbc0434e2eba43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14329b73af66646b981e106896efdc10.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-21更新
|
946次组卷
|
7卷引用:北京市朝阳区2024届高三上学期期末数学试题
北京市朝阳区2024届高三上学期期末数学试题北京市陈经纶中学2023-2024学年高一下学期阶段性诊断(3月)数学试卷(已下线)重难点4-1 平面向量的最值与范围(4题型+满分技巧+限时检测)(已下线)考点2 平面向量基本定理及坐标表示 --2024届高考数学考点总动员【讲】天津市第四十七中学2023-2024学年高一下学期第一次阶段性检测(3月)数学试题(已下线)【一题多变】定比分点 数乘求解(已下线)【讲】 专题二 与平面给向量数量积有关的范围与最值问题(压轴大全)
4 . 对于函数
,记所有满足
,都有
的函数构成集合
;所有满足
,都有
的函数构成集合
.
(1)分别判断下列函数是否为集合
中的元素,并说明理由,
①
;②
;
(2)若
(
)是集合
中的元素,求
的最小值;
(3)若
,求证:
是
的充分不必要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/264f35bf099b45c499c9529f61ce8579.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c7d35c770f126de82f6160bcfff0ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d928af44759824e38d2254270b1e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5ceb8c88f1b42f009d17854744d208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)分别判断下列函数是否为集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d01cb00904ee16178c7c35d7e0a8d3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba87ca31345dd12f5604d35f3c326a40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c532b5af7b88f1c21a7584cfac5fea6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd04b625189228b6d697edf095f7c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414c7ae60baeadabe19cd4a953522437.png)
您最近一年使用:0次
5 . 记函数
的定义域为
,若存在非负实数
,对任意的
,总有
,则称函数
具有性质
.
①所有偶函数都具有性质
;
②
具有性质
;
③若
,则一定存在正实数
,使得
具有性质
;
④已知
,若函数
具有性质
,则
.
其中所有正确结论的序号是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380348dd1544f954255976659a84a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
①所有偶函数都具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba837ccb2f36f9dcef19706e5a1f27.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69f66053a4d4a52740ee1e0c85dcc147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f276904f1527f7fc44e53889d1aabc03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701e586b9fc139bab7908dcd66e2afbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e711b6e5b2799dbff26742f4b70416.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
6 . 已知集合
,其中
且
,非空集合
,记
为集合B中所有元素之和,并规定当
中只有一个元素
时,
.
(1)若
,写出所有可能的集合B;
(2)若
,且
是12的倍数,求集合B的个数;
(3)若
,证明:存在非空集合
,使得
是
的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcbde10b7bc82536072ca38f32b2f8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cca1d86c9f078347773f700fee49d1d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe11d564517c04437b9884da859002b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9bc3a22bc9cb056df1e6d5218877c8c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6e90ea92c80c31653e4ac972bf56c8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d725be6acff620b47bb7a8a7a0c6e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af5e68b8592c14157df8db05904c8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fd9ec9c065d4337a8b1ebf2abc6a1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
您最近一年使用:0次
2024-01-20更新
|
324次组卷
|
2卷引用:北京市朝阳区2023-2024学年高一上学期期末质量检测数学试题
7 . 在一定通风条件下,某会议室内的二氧化碳浓度c随时间t(单位:
)的变化规律可以用函数模型
近似表达.在该通风条件下测得当
时此会议室内的二氧化碳浓度,如下表所示,用该模型推算当
时c的值约为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e008ee8b0dc593ce21d8d4c87afef1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ddb814f83a6f0c734266dc73d015a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32b6ffcdd8e21706cfe5df028f65a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d106a430e7748a4d596401820b9abd8.png)
t | 0 | 5 | 10 |
c | ![]() | ![]() | ![]() |
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知数列
.给出下列四个结论:
①
;
②
;
③
为递增数列;
④
,使得
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6ae84861f0ce9b88cfdd7e6ea04bb5.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c717b7ee0ad6e14a4823501cb4cf095.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdab278e1cc11f1dd34dada10d37402.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8194a62bc60a9da9b5cf76f9dc0fa09.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487ed36ad28abe16a9d5b4a8e7626a62.png)
其中所有正确结论的序号是
您最近一年使用:0次
名校
解题方法
9 . 已知各项均为正整数的有穷数列
:
满足
,有
.若
等于
中所有不同值的个数,则称数列
具有性质P.
(1)判断下列数列是否具有性质P;
①
:3,1,7,5;②
:2,4,8,16,32.
(2)已知数列
:2,4,8,16,32,m具有性质P,求出m的所有可能取值;
(3)若一个数列
:
具有性质P,则
是否存在最小值?若存在,求出这个最小值,并写出一个符合条件的数列;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1744df02bafb001642e47c96a41a7067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab6bff55e280804acd75acc5f154fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918f5fab265aa6e60eccab6800676838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(1)判断下列数列是否具有性质P;
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f762938f5c78eb72bafbb13bf85cba1.png)
(3)若一个数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e1823d02690076de1a1c45d7725ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11075f2c574b6c59b97fb3038000e38.png)
您最近一年使用:0次
2024-01-19更新
|
449次组卷
|
4卷引用:北京市东城区2023-2024学年高二上学期期末统一检测数学试卷
10 . 如图,正方形
的边长为1,连接
各边的中点得到正方形
,连接正方形
各边的中点得到正方形
,依此方法一直进行下去.记
为正方形
的面积,
为正方形
的面积,
为正方形
的面积,……..
为
的前
项和.给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/c953b28a-410f-4e09-8ec2-bc4ac20a0ddb.png?resizew=142)
①存在常数
,使得
恒成立;②存在正整数
,当
时,
;③存在常数
,使得
恒成立;④存在正整数
,当
时,
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a8012195f63ecbb610ba810a806103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64a8012195f63ecbb610ba810a806103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/6/c953b28a-410f-4e09-8ec2-bc4ac20a0ddb.png?resizew=142)
①存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ca7e3eede8f49b5aeec8f21dfe5411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f36a43e6b2660feaf82c88db905ede.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4eadb6761fe3c3c8dde8bdb1631e40e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f555bcf970e76c33f66e2cbc4a11764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ef124353a6e8f7a699086e5fd8e329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985dc26a89252b2e8dea815c529a2ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c751cf56508033b752972ffaec70121f.png)
您最近一年使用:0次
2024-01-19更新
|
271次组卷
|
3卷引用:北京市东城区2023-2024学年高二上学期期末统一检测数学试卷
北京市东城区2023-2024学年高二上学期期末统一检测数学试卷重庆市万州二中教育集团2023-2024学年高二下学期入学质量监测数学试题(已下线)第4章 数列 单元综合检测(难点)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)