1 .
的外接圆与内切圆分别为
、
,
为
旁切圆.
1.证明:存在唯一圆
,
与
内切、与
外切,并且与
内切于点A.
2.设圆
与
、
的切点分别为P、Q.如果
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d593e8cb8219aad703d77d78ef2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18a8ab9c2421408d202361aca2c944fb.png)
1.证明:存在唯一圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d593e8cb8219aad703d77d78ef2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
2.设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55b59c92a868cc6f448e5d92d257401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843d593e8cb8219aad703d77d78ef2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b746a5add435fea2d4d75c7479f01e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
您最近一年使用:0次
解题方法
2 . 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
3 . 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)
您最近一年使用:0次
4 . 设
,满足
.
(1)证明:若
,则当
时,
.
(2)若存在
满足
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e761714f6940c2c06c5750e2ed80cc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbd27b6b4143c730ab9d36393a5fe14.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c61cfbfd3bf888856b7dc9b2a84c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac247d375e0da7fddafad1aa8186aa51.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4439c7de7291f79def06d548603de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
您最近一年使用:0次
5 . 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
|
154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
6 . 已知函数
(
为常数)的图象上存在四个点
,过
的切线为
,其中
,且
围成的图形是正方形.
(1)求证:
;
(2)试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388c0990291dfcf9ce3060c06ddd810d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f70db67d96a5bf6d5c6b93ed64952d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb886661302d1bc974b0c4f2458fcea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693dd24614173c8295bc7cf97fd5725a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7122f2ae84bff5b73095f78cafe04f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64dafa5de92d59009eda97f12ac5d71.png)
(2)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
7 . 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
8 . 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
9 . 对三次函数
,如果其存在三个实根
,则有
.称为三次方程根与系数关系.
(1)对三次函数
,设
,存在
,满足
.证明:存在
,使得
;
(2)称
是
上的广义正弦函数当且仅当
存在极值点
,使得
.在平面直角坐标系
中,
是第一象限上一点,设
.已知
在
上有两根
.
(i)证明:
在
上存在两个极值点的充要条件是
;
(ii)求点
组成的点集,满足
是
上的广义正弦函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3037bb4ec2e6dfb182b22df30899cab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2dfbd59c0d4efc09e09ad82e83e431.png)
(1)对三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2c831570d29c0fcbe5da38473ee828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d6fa911e3396b34fb470c10b063fde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7121bf913ba5f136cb6d35db030ed70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c287a0f6a3521b83db37422a1aa309bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/944ede342597c070831052dc06bca45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe4d0e11cd9b9421c4d18121ffd181a.png)
(2)称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7041eb865c44a89770acd4fd71024bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9919ff015350c4e25aa0c05c09c329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b56f913087e3bbf8cd9dd7c9bba7dc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c65d3d6119b18fd2427497cbd413c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2232cbe8d56d936da2ea9c3a78d87f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce43981e5251e382690797f24907de2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d97b51756740950b8a9304755b4224.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42027a6a90b0a513981ebd5ed4431460.png)
(ii)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fa6d6bca6428b15c6e95504904e944.png)
您最近一年使用:0次
10 . 称
是
的一个向往集合,当且仅当其满足如下两条性质:(1)任意
,
;(2)任意
和
,有
.任取
,称包含
的最小向往集合称为
的生成向往集合,记为
.
(1)求满足
的正整数
的值;
(2)对两个向往集合
,定义集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbe16b433635b8bc25f303863807b70.png)
(i)证明:
仍然是向往集合,并求正整数
,满足
;
(ii)证明:如果
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160af7e0b1d01eec9b33474b4d067a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2077e5032491293f8181c4fc3bcf360a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ad11a8563df9a39fbe386f746f755c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8104c761c3fac71e51c9a17a154829ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27e8b43153beb780aa92d61df4b0da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60cfb0de87efce8d98d89106fd36f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8060d3a485605dd9fedb3c5ae089c24e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8f38fd2a2457ab28745c41c0f6b0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
(1)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c248f486fa233098501ba2a64422118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对两个向往集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0248166f5a50eb4fe7f8a02a2d8e397e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbe16b433635b8bc25f303863807b70.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a13c9838a7aa389c93dcbaf5ad0449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb92321829e1fa81061502157411cec.png)
(ii)证明:如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528af17b6a22c9c808c4231ef395a0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0161489025ecbc391b1c9affce57b930.png)
您最近一年使用:0次