名校
1 . 对于正整数集合
,如果去掉其中任意一个元素
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“平衡集”.
(1)判断集合
是否是“平衡集”并说明理由;
(2)求证:若集合
是“平衡集”,则集合
中元素的奇偶性都相同;
(3)证明:四元集合
,其中
不可能是“平衡集”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbfa3e226e067ec597ebf0bbc2e87d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c4392f75c09edaec2e70c9eccb2b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5f6cb6141a374d04b6a14a1b27e282.png)
(2)求证:若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)证明:四元集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a784e0ba1c17aba6990123fe39b89114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a3f266cb6beee27f3d831c1169d3d2.png)
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2 . 对任意正整数n,记集合
,
.
,
,若对任意
都有
,则记
.
(1)写出集合
和
;
(2)证明:对任意
,存在
,使得
;
(3)设集合
.求证:
中的元素个数是完全平方数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39352d44787ecda055946f530893f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5359f5f086b89cc656cdd4f79a3b7baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df0913f90131b298c8f6f57437f69b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c1352dca7dc3caf67c1cb937d52795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35755ad07f05e7bfe00176d6334389f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75a28908216e6879a09b372d957be1e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
(1)写出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e840ba7606959ccea36793f3ef0775d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b576952835af1f3492f0f3e6d00093e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90df641ab645927ee577e79faf18dcdd.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/112d102cbe7ce2bebe0c76e87e89a00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-11-15更新
|
158次组卷
|
4卷引用:北京市第三十五中学2023-2024学年高二上学期期中考试数学试题
名校
3 . 对于正整数集合
,如果去掉其中任意一个元素
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“和谐集”.
(
)判断集合
是否是“和谐集”(不必写过程).
(
)请写出一个只含有
个元素的“和谐集”,并证明此集合为“和谐集”.
(
)当
时,集合
,求证:集合
不是“和谐集”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9a40d9006d3e9ef471da620a636b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e053f60d2756b7d952f4fd3d547c12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b07a67307d5d4627efa688b30e5573.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ec5e58ce0ca1d903b509043df31a6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2018-07-02更新
|
1560次组卷
|
8卷引用:【全国百强校】北京东城北京二中2017-2018学年高二上学期期中考试数学(理)试题
【全国百强校】北京东城北京二中2017-2018学年高二上学期期中考试数学(理)试题北京市西城区北京师范大学第二附属中学2021-2022学年高一上学期期中数学试题北京市大峪中学2022-2023学年高一上学期期中考试数学试题北京市人大附中北京经济技术开发区学校2023-2024学年高一上学期期中考试数学试题人教A版(2019) 必修第一册 突围者 第一章 易错疑难集训(一)(已下线)1.2集合间的基本关系-2021-2022学年高一数学同步辅导讲义与检测(人教A版2019必修第一册)(已下线)高一上学期期中【压轴60题考点专练】(必修一前三章)-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)(已下线)期中真题必刷压轴60题(15个考点专练)-【满分全攻略】(人教A版2019必修第一册)
名校
4 . 设正整数
,若由实数组成的集合
满足如下性质,则称
为
集合:对
中任意四个不同的元素
,均有
.
(1)判断集合
和
是否为
集合,说明理由;
(2)若集合
为
集合,求
中大于1的元素的可能个数;
(3)若集合
为
集合,求证:
中元素不能全为正实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead6fe08a80379f496eab2129655bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be0f5b704e46d64481197273b2e2557.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ccef0bee54b52b069616251fbea584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9cba4a6e473e359492361f51d8556a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def70b21b73d0d0156f8ffb526413d97.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37fb28a9d01dfd12b13bce4ac4c3c5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def70b21b73d0d0156f8ffb526413d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead6fe08a80379f496eab2129655bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-01-19更新
|
211次组卷
|
2卷引用:北京市朝阳区2023-2024学年高二上学期期末质量检测数学试题
5 . 阅读下面题目及其解答过程.
以上题目的解答过程中,设置了①~⑤五个空格,如下的表格中为每个空格给出了两个选项,其中只有一个正确,请选出你认为正确的选项,并填写在答题卡的指定位置(只需填写“A”或“B”),
已知函数![]() (1)证明: ![]() (2)证明: ![]() ![]() 解:(1) ![]() ![]() 因为对任意 ![]() ![]() ![]() ![]() (2)③________ ![]() ![]() ![]() ![]() ![]() ![]() 因为 ![]() 所以 ![]() ![]() ![]() 所以 ![]() ![]() 所以 ![]() ![]() |
空格序号 | 选项 |
① | A.![]() ![]() |
② | A.![]() ![]() |
③ | A.任取 B.存在 |
④ | A.![]() ![]() |
⑤ | A.![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 给定正整数
,设集合
.对于集合
中的任意元素
和
,记
.设
,且集合
,对于
中任意元素
,若
则称
具有性质
.
(1)判断集合
是否具有性质
?说明理由;
(2)判断是否存在具有性质
的集合
,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5f57a82532efc3493710a2ff44fefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94a6d1701e8172b86bc880c24d0bc58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8eb800ed1a7e5e22e3947e6bd30c87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35e477c52dfbfb80f1fc315143c8b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1368a045ba80f97383f3d9d7fcdc8f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae454efa6255bf3bb1c43e845746088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9855cb665c7f3785a17718be10538af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2f08194bb663f1a086fa2f555ebf43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5651757f34e9de2462ccdc056f04ab4.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2fbba9715be4e3cb0886973e3d3ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25c874d4ce0667f3acfe8d26d2a5b6f.png)
(2)判断是否存在具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d0e79b3bb773de1ebea52199754c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-01-25更新
|
305次组卷
|
4卷引用:北京市海淀区北京交通大学附属中学2023-2024学年高二上学期期中练习数学试题
北京市海淀区北京交通大学附属中学2023-2024学年高二上学期期中练习数学试题北京市延庆区2023-2024学年高二上学期期末考试数学试卷(已下线)专题04 分类讨论型【讲】【北京版】2(已下线)专题1 集合新定义题(九省联考第19题模式)练
7 . 设
,如果函数
:
的值域也是
,则称之为一个泛函数,并定义其迭代函数列
:
,
.
(1)请用列表法补全如下函数列;
(2)求证:对任意一个
,存在正整数
(
是与
有关的一个数),使得
;
(3)类比排序不等式:
,
,把
中的10个元素按顺序排成一列记为
,使得10项数列
:
,
,
,…,
的所有项和
最小,并计算出最小值
及此时对应的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0367345901c5a716dca179385158c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84315a088ff3d8b91be22d3b3fcd92ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99442281052744a6b74b32e0fc2536f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66a88cbaed58dcf9671ba9240359b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b2c1a76a73797e9d5699f6c9929a50.png)
(1)请用列表法补全如下函数列;
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
2 | 1 | 7 | 5 | 3 | 4 | 9 | 10 | |||
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002bda38860f9cbc17dd7b6a03cfecf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d5926ad4ccd91c0ec7ff14018de8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5328785361a76b5e8f75b034a07c5e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b526c87ad796e8cd189f88c33c8d8fd.png)
(3)类比排序不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109ae0739494164db5b7edae7bfb2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd643dcc6985a78b5dfe3127610e920e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eee7088c883282e2f7d95a1856902fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87139b2d092ad22a082bd2a9fa31901d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4aac3646575e397de3dee4ed5d1060b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f27bc508f582e07211ee24d01bc551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77ac9dd1c3046137614c0f62e55190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd643dcc6985a78b5dfe3127610e920e.png)
您最近一年使用:0次
名校
8 . 设
,已知由自然数组成的集合
,集合
,
,…,
是
的互不相同的非空子集,定义
数表:
,其中
,设
,令
是
,
,…,
中的最大值.
(1)若
,
,且
,求
,
,
及
;
(2)若
,集合
,
,…,
中的元素个数均相同,若
,求
的最小值;
(3)若
,
,集合
,
,…,
中的元素个数均为3,且
,求证:
的最小值为3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1221e342a03bd2806e0993c996827ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abc7b7ef8b7a91099ca63ea1aaf7cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6571a9572dc91c90da43a5390f69d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b2c4a940739711008be65a1fad4146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ac1a105450fef08656cf15a10e7fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47771d50cf28b8f528afda24720eb8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52ce6355f8b297a89f20f2e7f48041d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5beea8e2b24bdc221f6c16e46efdf665.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862353b1d19b5e38a60c4ceeb2b01913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4e4ea995fa993d6a55c2e523fa8ae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad28732b9ef03fa2a2fcabe344c27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caddd958ae597c7a1f8f6a9ee2a3200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
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2023-07-10更新
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661次组卷
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4卷引用:北京市陈经纶中学2023-2024学年高二上学期开学检测数学试题
北京市陈经纶中学2023-2024学年高二上学期开学检测数学试题北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列
名校
9 . 已知自然数集
,非空集合
.若集合E满足:对任意
,存在
,使得
,称集合E为集合A的一组m元基底.
(1)分别判断下列集合E是否为集合A的一组二元基底,并说明理由:
①
;
②
.
(2)若集合E是集合A的一组m元基底,证明:
;
(3)若集合E为集合
的一组m元基底,求m的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcaa2be7b1653f2371891e9a794f023d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5002b44e87e59f1e1fda6a841de5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c059a6234c274a3aa626b20698263c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53613f4c8d697ad45bd08f29ef76f19e.png)
(1)分别判断下列集合E是否为集合A的一组二元基底,并说明理由:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c93b026b2bd1f754bcee49e48c6bbb4.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3210812ece496c3ab3396e9ec2f0c6e.png)
(2)若集合E是集合A的一组m元基底,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e41403eba28ee0f497c79953b842ca1.png)
(3)若集合E为集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1341ae10a275cd370eb014d0f505f3.png)
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2023-11-03更新
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2卷引用:北京市人大附中2023-2024学年高二上学期期中数学试题
名校
解题方法
10 . 设A是正整数集的一个非空子集,如果对于任意
,都有
或
,则称A为自邻集.记集合
的所有子集中的自邻集的个数为
.
(1)直接写出
的所有自邻集;
(2)若
为偶数且
,求证:
的所有含5个元素的子集中,自邻集的个数是偶数;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417abc71b8bee465746db0a35e776f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca2371b88985463ba25e4ec1ea453d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377240e8ad277805e0499803d5be5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623eef12f37f0b85ddd367faa9b3bfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aba3402e1d191ff96adda7c4af70ef.png)
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2023-05-28更新
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11卷引用:北京市第五十七中学2021-2022学年高二上学期期中检测数学试题
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