真题
名校
1 . 已知
,函数
,记
为
的从小到大的第![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
个极值点,证明:
(1)数列
是等比数列
(2)若
,则对一切
,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e4d33f1bf9890db710addddec09df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31419e0523278fb897fc050d234e9f8.png)
(1)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3998deeec91b7dc0f51977d3254b1954.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4910b4023f1340e89c482fe2022ceaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da75f19e26f1380aaa55f854eebd6f3.png)
您最近一年使用:0次
2016-12-03更新
|
3383次组卷
|
5卷引用:2015年全国普通高等学校招生统一考试理科数学(湖南卷)
2015年全国普通高等学校招生统一考试理科数学(湖南卷)(已下线)考点11 导数与函数的单调性,极值,最值-2021年新高考数学一轮复习考点扫描湖南省长郡中学2023届高三下学期月考(七)数学试题(已下线)专题22 导数解答题(理科)-3专题35导数及其应用解答题(第二部分)
2 . 已知常数
,函数
.
(1)讨论
在区间
上的单调性;
(2)若
存在两个极值点
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a78faf3b395f0aa3c26e058458f4a45.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e881fec40d166eecf66123058faf05fe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedfd6ca00eb881176da40a6305e2743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2016-12-03更新
|
5192次组卷
|
15卷引用:2014年全国普通高等学校招生统一考试理科数学(湖南卷)
2014年全国普通高等学校招生统一考试理科数学(湖南卷)湖南省长沙市长郡中学2017-2018学年高三上学期第一次月考理科数学试题湖南省衡阳市衡东县欧阳遇实验中学2018-2019学年高二下学期期末数学试题广东省阳春市第一中学2018届高三上学期第二次月考数学(理)试题.河北省衡水中学2018届高三三轮复习系列七-出神入化5数学(理)试题(已下线)2019高考备考一轮复习精品资料 【理】专题十五 导数的综合应用 教学案(已下线)2019高考热点题型和提分秘籍 【理数】专题11 导数的应用 (教学案)(已下线)2019高考热点题型和提分秘籍 【文数】专题11 导数的应用 (教学案)【全国百强校】北京市海定区101中学2018-2019学年高二年级下学期期中考试数学试题福建省莆田第一中学2018-2019学年高二下学期期中数学(理)试题陕西省西安市八校2020届高三(6月份)高考数学(理科)联考试卷陕西省西安地区2020届高三下学期八校联考理科数学试题河北省石家庄市二十七中2021-2022学年高二下学期期中数学试题天津市蓟州区第一中学2023-2024学年高三上学期第一次学情调研数学试题(已下线)专题22 导数解答题(理科)-2
真题
名校
3 . 如图,
为坐标原点,双曲线
和椭圆
均过点
,且以
的两个顶点和
的两个焦点为顶点的四边形是面积为2的正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/3268bbb0-436c-4260-bbf5-01b6a0823fd0.png?resizew=204)
(1)求
的方程;
(2)是否存在直线
,使得
与
交于
两点,与
只有一个公共点,且
?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43cadb6f88905d3f9f5847bcab281863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1cc1fada76e2dc8bedfe8fe1e275b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25040a22387f7a45dd2879b9f9e7a39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/3268bbb0-436c-4260-bbf5-01b6a0823fd0.png?resizew=204)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)是否存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472fcc8bf0efbc3546a4fa8bbb86e9b7.png)
您最近一年使用:0次
2016-12-03更新
|
4503次组卷
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3卷引用:2014年全国普通高等学校招生统一考试文科数学(湖南卷)
真题
4 . 已知函数
.
(1)求
的单调区间;
(2)记
为
的从小到大的第
个零点,证明:对一切
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f967281e8a174e59c38c962ffa56a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13aa77366455a0a5c1dcccccd633fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5235e9027fd05f69f760241e8f08a13c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea0cbf208441628800b02e09046c807.png)
您最近一年使用:0次
真题
名校
5 . 已知数列
满足
,
.
(1)若
为递增数列,且
成等差数列,求
的值;
(2)若
,且
是递增数列,
是递减数列,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28dbfa38d09eb8228c1503a374c7ee6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d726666f99a5a41dd673a2330e377b17.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccadf5fe0d8a09ac97324ad2d9f60f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc383c64f1182577bc35c8ec69efd815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd73bb86944362b433be016d442f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
您最近一年使用:0次
2016-12-03更新
|
3675次组卷
|
10卷引用:2014年全国普通高等学校招生统一考试理科数学(湖南卷)
2014年全国普通高等学校招生统一考试理科数学(湖南卷)2015-2016学年安徽省合肥市一六八中高二上开学考试理科数学试卷2016-2017学年广东清远三中高二上学期第一次月考数学(理)试卷2018届高三数学训练题(38):等比数列 人教A版 成长计划 必修5 第二章数列 高考链接上海市上海中学2017-2018学年高三下学期5月适应性考试数学试题(已下线)专题17 数列的概念与数列的通项公式-十年(2011-2020)高考真题数学分项湖南省常德市第一中学2023届高三下学期第十一次月考数学试题(已下线)专题8 等比数列的单调性 微点1 判断等比数列单调性的方法(已下线)专题21 数列解答题(理科)-1
6 . 如图,
为坐标原点,椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a259dddccc3cfe8f81735cd5834785d.png)
的左右焦点分别为
,离心率为
;双曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf1bce17440e83c1b735d2954010a2a.png)
的左右焦点分别为
,离心率为
,已知
,且
.
(1)求
的方程;
(2)过
点作
的不垂直于
轴的弦
,
为
的中点,当直线
与
交于
两点时,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a259dddccc3cfe8f81735cd5834785d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf1bce17440e83c1b735d2954010a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626706e779756baf8f7aa4cd276d2017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e749c051ebeba72d9873b4f31c8ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4aed953f852a8f9eab33645b2078dc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d4ab45e8e8f0084d8d90a4c1233d86.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/28/eb8915cc-1337-4d04-a350-edd99f29bb3a.png?resizew=262)
您最近一年使用:0次
2016-12-03更新
|
6731次组卷
|
6卷引用:2014年全国普通高等学校招生统一考试理科数学(湖南卷)
2014年全国普通高等学校招生统一考试理科数学(湖南卷)四川省成都外国语学校2017-2018学年高二下学期入学考试数学(理)试题(已下线)专题30 圆锥曲线三角形面积与四边形面积题型全归类-2(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)重庆市第十八中学2023-2024学年高二上学期12月学习能力摸底数学试题(已下线)专题24 解析几何解答题(理科)-3
7 . 对于E={
,
,…,
}的子集X={
,
,…,
},定义X的“特征数列”为
,
,…,
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e5ee0eaeb1b74999cc0a9a9f244545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f21c970d5c427466f9dc79b278003f.png)
=1.其余项均为0,例如子集{
,
}的“特征数列”为0,1,1,0,0,
,0 ,则子集{
,
,
}的“特征数列”的前三项和等于________________ ;若E的子集P的“特征数列”
,
,…,
满足
,
1≤i≤99;E 的子集Q的“特征数列”
,
,…,
满足
=1,
,1≤j≤98,则
的元素个数为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89fe44dab672c37b60f97de0040be87a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8569a9c44c8848428cf81adc03d4151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da71ee409fbba26c08c826f6137ba6ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67813342a0f27a1a3a5804b6b48021a7.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/53e4c6544ede4573bd9a07d116f5cfb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e5ee0eaeb1b74999cc0a9a9f244545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f21c970d5c427466f9dc79b278003f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f51f2e6783cd5fd17c4496e966c452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be646cd52d7f2f1714e7542e75810f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b92cba1ed694b1a11411fa274ff7c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e5cfb0d2cf24c1da7ba972e0218a974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc1a195f904c8292c2db380466d139f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171ff5c2728e7cf00a88f88de14f308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c02e55edaf83351e20283be2048b0a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6268630d5e5288048d32f4aa5c8bc02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97479eeeb877265dd63307c9460abd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4afabfd5b4885311f8d9a4bcf791b71.png)
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8 . 过抛物线
的焦点F作斜率分别为
的两条不同的直线
,且
,
相交于点A,B,
相交于点C,D.以AB,CD为直径的圆M,圆N(M,N为圆心)的公共弦所在的直线记为
.
(I)若
,证明;
;
(II)若点M到直线
的距离的最小值为
,求抛物线E的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a69ab234c3a8a40a9d0a9620df498af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec7bcf5820dfe70290259c2d7ac1ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe42865a8ca3fe91e104273a4174e079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46fbee1091c01d2752d3ec2e804bf9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90931781b834d100def5e571c28486db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc119913022c0911844ab30307982a41.png)
(II)若点M到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97814cbb7a07b2e5726d144f97ebf444.png)
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2016-12-02更新
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3129次组卷
|
3卷引用:2013年全国普通高等学校招生统一考试理科数学(湖南卷)
真题
9 . 对于
,将n表示为
,当
时
,当
时
为0或1,定义
如下:在
的上述表示中,当
,a2,…,ak中等于1的个数为奇数时,bn=1;否则bn=0.
(1)b2+b4+b6+b8=__ ;
(2)记cm为数列{bn}中第m个为0的项与第m+1个为0的项之间的项数,则cm的最大值是___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010306e32014676fdb0faf1a2b9327c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1526a35c87ee4331c1b1be81d9dd2ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4988a9309359e790f4750d640a615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb16f039613ef12dbf6fcf5801b2eda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016931f7abd87a3e11e0790926230ebf.png)
(1)b2+b4+b6+b8=
(2)记cm为数列{bn}中第m个为0的项与第m+1个为0的项之间的项数,则cm的最大值是
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10 . 设N=2n(n∈N*,n≥2),将N个数x1,x2,…,xN依次放入编号为1,2,…,N的N个位置,得到排列P0=x1x2…xN.将该排列中分别位于奇数与偶数位置的数取出,并按原顺序依次放入对应的前
和后
个位置,得到排列P1=x1x3…xN-1x2x4…xN,将此操作称为C变换,将P1分成两段,每段
个数,并对每段作C变换,得到
;当2≤i≤n-2时,将Pi分成2i段,每段
个数,并对每段C变换,得到Pi+1,例如,当N=8时,P2=x1x5x3x7x2x6x4x8,此时x7位于P2中的第4个位置.
(1)当N=16时,x7位于P2中的第___ 个位置;
(2)当N=2n(n≥8)时,x173位于P4中的第___ 个位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28500c2dcb4234c2bf18737939725670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24879b60db93a877f50cdbd8edf557d.png)
(1)当N=16时,x7位于P2中的第
(2)当N=2n(n≥8)时,x173位于P4中的第
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