解题方法
1 . 对集合
,定义其特征函数
,考虑集合
和正实数
,定义
为
和式函数.设
,则
为闭区间列;如果集合
对任意
,有
,则称
是无交集合列,设集合
.
(1)证明:L和式函数的值域为有限集合;
(2)设
为闭区间列,
是定义在
上的函数.已知存在唯一的正整数
,各项不同的非零实数
,和无交集合列
使得
,并且
,称
为
和式函数
的典范形式.设
为
的典范数.
(i)设
,证明:
;
(ii)给定正整数
,任取正实数
和闭区间列
,判断
的典范数
最大值的存在性.如果存在,给出最大值;如果不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1304eb00ab95d664dc84385f602a8f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee6c8ae5004f2ffe7f8392b4d3c39b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238908949859936af0e109ef684599b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c09d82c480e4d67f8a48d3f66c5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a02da5d46478a54d279755a295d548f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b56da93ba7a2dec958070eb2666240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05386869739fb11a190c637ba8a93174.png)
(1)证明:L和式函数的值域为有限集合;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fa51de98f090eda3e3f60a26475db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfcda4333678bafacc4c676c2836977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee06844034f61cab7d421d55179ee367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359a16305129aeea0953efd9100f4b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b4e32041b54703ade8e8c2cee01f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed82555c7d6fc6b449fbdb1f68fef1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
(i)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1462612f3654548c39489985987cb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870c36161f465fc992534b5fc3777f3.png)
(ii)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f69939291758b5eaa19146f76709e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b4010030e10725398b64d4dcc09429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
2 . 春节将至,又是一年万家灯火的团圆之时.方方正正的小城里,住着
户人家,恰好构成了坐标平面上集合
的所有点.夜里,小城的人家挂上大红灯笼,交相辉映,将小城的夜晚编织成发光的大网.在坐标平面上看,A中的每个点均独立地以概率p被点亮,或以
的概率保持暗灭.若A中两个点的距离为1,则这两个点被称为是相邻的.若A中的n个被点亮的点
构成一依次相邻的点列
,则称这n个点组成的集合
是长度为n的“相邻灯笼串”.规定空集是长度为0的“相邻灯笼串”.
(1)给定A中3个依次相邻的点
,记随机变量X为集合
包含的“相邻灯笼串”的长度的最大值,试直接写出随机变量X的分布列(用p表示);
(2)若
,证明:存在长度为1000的“相邻灯笼串”的概率小于0.01;
(3)若
,证明:存在长度为1000的“相邻灯笼串”的概率大于0.99.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ef6c862fe408c21f7779e4e8e82fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0c982180ad66af4330b1a8c43e4c07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae7fb954b47cb67fdde891c3b9d8295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce642b73be99b3c1a8c5dd38ec58eb28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e59f96c54b4a41ed3c5b33b44320b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e69a66f2a66f4cd0fa05f5bbe185b6b.png)
(1)给定A中3个依次相邻的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85555fed049f8bb454c7569904bfed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718d05f8dd704256c99ac978e1ad5336.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bea306bdd00e500a305816f378060e4.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47938ad49863a8ff60ea48d0820e48f4.png)
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3 . 设
是正实数数列.
(1)若
收敛,求证:存在严格递增的无界正实数数列
满足
收敛.
(2)若
收敛,是否一定存在严格递增的正整数数列
,满足
收敛,且
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7376941fa463c63b1d4d4ea866b78c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccecde965d7557d5ee35dea8ae7164a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c988a3683540149b687486af0ed3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120dcd9c3adc5b08ab9d84f228cc4b90.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ad99ac2f9cbe69281dcdc7d4195d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba58d775c69de6d132c58581d614792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246e5563a2f86de45879b21393d814f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c69eef9b8e90f6a153b87738f759bcf.png)
您最近一年使用:0次
4 . 在锐角
中,
为
延长线上一点,过
分别作
,
平行线
,
,若
,
,且
的外接圆与
交于点
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5161dac60a307b5768018875063deaac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d61be62a066c7ad65f9fa64ba1de1ba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d172d77168b66134a5a852412d4f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a6af45c7f8453cf711317ffe66dccec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345f52e0835cc13f92b6801169105a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4c6b0869d7248b6c2f964718a67702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b0424af44604f489a804efb1e4b28a0.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940730a19110cc363c871e0599388e56.png)
您最近一年使用:0次
2023-12-14更新
|
152次组卷
|
2卷引用:2023年第39届全国中学生冬令营(CMO)数学试题
5 . 校乒乓球锦标赛共有
位运动员参加.第一轮,运动员们随机配对,共有
场比赛,胜者进入第二轮,负者淘汰.第二轮在同样的过程中产生
名胜者.如此下去,直到第n轮决出总冠军.实际上,在运动员之间有一个不为比赛组织者所知的水平排序,在这个排序中
最好,
次之,…,
最差.假设任意两场比赛的结果相互独立,不存在平局,且
,当
与
比赛时,
获胜的概率为p,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a998c92f966aae015d3e1e37c967e7b5.png)
(1)求最后一轮比赛在水平最高的两名运动员
与
之间进行的概率.
(2)证明:
,
为总冠军的概率大于
为总冠军的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31971306914638e5ceb1bbe437535d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f1ad18371ec533aeac27cf1fad95c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cc8f06c961b64b15a90b99f7adc604.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/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519321dbfc38d9b89948762478f71d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9454ddb2d570f884b15bd3ddf2a4545d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6ba141730fd5aae78ada1a8eb17d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a998c92f966aae015d3e1e37c967e7b5.png)
(1)求最后一轮比赛在水平最高的两名运动员
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae64cb0b1c5e4f556e0ee0ca54fa9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5654866bd68198db845fb43c6b4c858.png)
您最近一年使用:0次
解题方法
6 . 离散对数在密码学中有重要的应用.设
是素数,集合
,若
,记
为
除以
的余数,
为
除以
的余数;设
,
两两不同,若
,则称
是以
为底
的离散对数,记为
.
(1)若
,求
;
(2)对
,记
为
除以
的余数(当
能被
整除时,
).证明:
,其中
;
(3)已知
.对
,令
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05bea470ae14b90937f6f71dc9a6242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b2b0dcbc27df9950b26028e46f6c17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5865fd0fb7c35e8a4a1d311163290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbe6ebc6c1d1a214f5ca478ae666cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67a1f88ae28ecdb67c7f9c4ae61481b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dae890dd5b6300cf23b4905e86410317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff99d1615f90ff71b56ca1dfebd626d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420a12638f77a27c696f63ff946e8684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b0087ea124b6fd98fbbcb9bc4c2e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](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/9ce071bd0d6fa72ff4ba4e72d810d11f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac54185ed8bb89c774ceb685408156c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7b54c31c5ab3831f260012758ffa12.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099d389a1c0e5877350e62c52c4a724c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ab2ad5d8b72e3f26bef4be0697ec70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6b09b60bf1bf8403c49bc17e365cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ebb2233e8492cf61fe9f9bc68af470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6b09b60bf1bf8403c49bc17e365cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ebb2233e8492cf61fe9f9bc68af470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fc26e532b65641a53eaa7e127aa683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d45dbe0a914249371aed3641515123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ace23b21d7b119ad7ac5cf877c19f0.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce071bd0d6fa72ff4ba4e72d810d11f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2793be26b839ae9f8f83cf2b5a597cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a6740a4f2378965bc019bc6aacd44a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f278b4fd6ed264265e3ccfac4ab7ef02.png)
您最近一年使用:0次
2024-01-19更新
|
6528次组卷
|
8卷引用:2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题
2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题(已下线)2024年1月普通高等学校招生全国统一考试适应性测试(九省联考)数学试题变式题16-192024年九省联考试卷分析及真题鉴赏(已下线)压轴题高等数学背景下新定义题(九省联考第19题模式)讲(已下线)微考点8-1 新高考新题型19题新定义题型精选(已下线)新题型02 新高考新结构竞赛题型十五大考点汇总-2(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)专题8 考前押题大猜想36-40
7 . 已知多项式
.
(1)若
,且
有三个正实数根
,
,
,证明:
;
(2)对一般的正整数
,若
,
,
,
,证明:方程
的根不全是正实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d310b3ca60508199bb95f15860232f4d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8de1c943439d47ca9e9a02e558a1b2e.png)
(2)对一般的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9772498c845b2043b375d1e8d8416b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e506a31a62c9581edb62218fce59b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f13c73c7894077a19b6c403587de96a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4e01e8ef5adf43e1f21591adbc3851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
您最近一年使用:0次
23-24高三上·重庆·开学考试
名校
8 . 设函数
,
,
,且
有唯一零点.
(1)求a的取值范围;
(2)证明:
存在三个零点;
(3)记
的零点为p,
最小的零点为q,证明:
,其中e是自然对数的底数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199fc1eb0897f0d666542dd3edb0f07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a73103f8cea1007406c4f59a9a069ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求a的取值范围;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/631fc97fa76831f00c2e541c92903110.png)
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9 . 设k是正整数,集合A至少有两个元素,且
.如果对于A中的任意两个不同的元素x,y,都有
,则称A具有性质
.
(1)试判断集合
和
是否具有性质
?并说明理由;
(2)若集合
,求证:A不可能具有性质
;
(3)若集合
,且同时具有性质
和
,求集合A中元素个数的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196ee858814f200b4414975cc154f333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a33197acadf8491f921a9330f94260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
(1)试判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb1aca774c04bd0599d77a1c0c9b43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aabb4483ddc6e67b4fedb0e09518f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5d8bc28ee110a9540f383828b7d245.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad04af133fc5d09790cddd1c2c199892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41b85f6960a2a4f988e5ddd9ef48d0e.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d096a06a215ba878c07d26f801498aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0127f7421ce1839e335f091d730736af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677dcea09d90af109df9cc72cff15cf0.png)
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2023-05-10更新
|
832次组卷
|
3卷引用:北京市清华大学附属中学2022-2023学年高一下学期期中数学试题
北京市清华大学附属中学2022-2023学年高一下学期期中数学试题(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)北京市第三十五中学2023-2024学年高一上学期期中测试数学试题
2023高三·全国·专题练习
名校
10 . 已知由实数组成的数组
满足下面两个条件:
①
;②
.
(1)当
时,求
,
的值;
(2)当
时,求证
;
(3)设
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0766a9dd0058b52abd9ad17ddb04fc2c.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8126d64e2becb117d8d42af22a5919b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12927cb41f08b3fd18f338623db8d8d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24819c61a0a42291903e3c2f5e1c6e41.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7310dc844ccb33e0ff0b62aeb47b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818dfdff56f53b3ecfb1096a692e914d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb74763554fd459d736ed9c7b387e01.png)
您最近一年使用:0次