1 . 古希腊著名的约瑟夫环问题讲的是:共有127个士兵,围成一个环,从一号位的士兵开始,每个存活下来的人依次杀死相邻的下一位士兵,若一名叫做约瑟夫的士兵想要存活到最后,那么他最开始应当站在几号位上?( )
A.1 | B.63 | C.127 | D.31 |
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2 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a670e5d56fcdd3cc214064c5d3d3b1.png)
(1)当
时,解关于
的不等式
;
(2)若
有两个零点
,求
的值;
(3)当
时,
的最大值
,最小值为
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a670e5d56fcdd3cc214064c5d3d3b1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ef9f9f0a79e61a30f7da782cbb2fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6abf3f9b0ebcdc47a028c781b7edb9.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5f18a08ed6cf92b894ea722af72862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3 . 对于给定的一个
位自然数
(其中
,
),称集合
为自然数
的子列集合,定义如下:
{
且
,使得
},比如:当
时,
.
(1)当
时,写出集合
;
(2)有限集合
的元素个数称为集合
的基数,一般用符号
来表示.
(ⅰ)已知
,试比较
大小关系;
(ⅱ)记函数
(其中
为
这
个数的一种顺序变换),并将能使
取到最小值的
记为
.当
时,求
的最小值,并写出所有满足条件的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6be3d8ff4885ce8cf21ed3b7e4c9059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4ab89a62749697c6a67e4fe8e6f3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b0e3b00fe47801afb53ec56706c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5123cae73867329882792f626287b970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d688a7cacda715fc5c2fad9a2adaddee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab691edda624f588e85d493423b3e398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fb6d4810762396e3fbe728687a0794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7a9e06bedb3aca590121cc47e64e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e534ff8ca5451dce6629223e002d5878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d407ed5fd8a5fd413426fc1fc118422.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeaa1b4ec60977b69d48d3d023f5d731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5123cae73867329882792f626287b970.png)
(2)有限集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
(ⅰ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43ea4161df6e6178c26c524935af465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53fe2a5d83d2e3e97f3a49d1f845370.png)
(ⅱ)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2a7d5abc0e14bf1da403fba5b27644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c558c7204d256c96b74b9c991c0e5c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad1bf0868f56ad3bda73d4ca5851cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf91726683a3963e941231877c8c6ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e731e11a03c0f5d2768e87a3442634d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c326b4a68d5148e8e5a5ebc15d3b132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad1bf0868f56ad3bda73d4ca5851cb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e731e11a03c0f5d2768e87a3442634d.png)
您最近一年使用:0次
4 . 若
是一个集合,
是一个以
的某些子集为元素的集合,且满足:①
属于
,空集
属于
;②
中任意多个元素的并集属于
;③
中任意多个元素的交集属于
,则称
是集合
上的一个拓扑.已知函数
,其中[x]表示不大于
的最大整数,当
时,函数
值域为集合
,则集合
上的含有4个元素的拓扑
的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a837165ca03f9e4ea8964979c95e3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89d1c17a43495542eaade6426cf4c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668efc94065bc0b990673bf77c40eeeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
2024-04-29更新
|
180次组卷
|
2卷引用:浙江省温州新力量联盟2023-2024学年高二下学期4月期中考试数学试题
5 . 若关于
的方程
的整数根有且仅有两个,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63550f448d55ec10d2754d3a6f54ec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
6 . 如图,对于曲线
,存在圆
满足如下条件:
①圆
与曲线
有公共点
,且圆心在曲线
凹的一侧;
②圆
与曲线
在点
处有相同的切线;
③曲线
的导函数在点
处的导数(即曲线
的二阶导数)等于圆
在点
处的二阶导数(已知圆
在点
处的二阶导数等于
);
则称圆
为曲线
在
点处的曲率圆,其半径
称为曲率半径.
(1)求抛物线
在原点的曲率圆的方程;
(2)求曲线
的曲率半径的最小值;
(3)若曲线
在
和
处有相同的曲率半径,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
②圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80999542b0b1e42a23e95363667399a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92637a7e7dab461f173112dfc8fa7390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b40504aef42ec81163e9581efbd83b.png)
则称圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
(3)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3c0b12482cc93dee05fbf69350cd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f455ecf39764829b0bfe0a8675f1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbd8e10a553d5607bb8906b2cf64aaf.png)
您最近一年使用:0次
名校
解题方法
7 . 已知
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6808c268db93fe1affa8cccffa9390d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
8 . 已知
,函数
在点
处的切线均经过坐标原点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a72228506f0ab7d8d4179fd0ca82d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa89a2010f813feaaf42256d0742f71a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-04更新
|
2635次组卷
|
7卷引用:浙江省温州市2024届高三上学期期末考试数学试题
浙江省温州市2024届高三上学期期末考试数学试题湖南省2024届高三数学新改革提高训练五(九省联考题型)安徽省阜阳市阜阳一中2023-2024学年高二下学期开学检测数学试题(已下线)新题型01 新高考新结构二十一大考点汇总-3上海市浦东新区上海实验学校2024届高三下学期开学考试数学试题(已下线)黄金卷02(2024新题型)甘肃省兰州市西北师范大学附属中学2024届高三第三次诊断考试数学试题
9 . 已知
.
(1)若过点
作曲线
的切线,切线的斜率为2,求
的值;
(2)当
时,讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ecf1868ef98213091efb8049e9beb45.png)
(1)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da7544af9e0d48ac4a99c8d5290f789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538193a4717d564c01145e82314c2d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7729eede7193f9bf6110bf9d39773c.png)
您最近一年使用:0次
2024-01-25更新
|
970次组卷
|
5卷引用:浙江省温州市温州中学2024届高三第一次模拟考试数学试题
浙江省温州市温州中学2024届高三第一次模拟考试数学试题山西省长治市2023-2024学年高二上学期1月期末数学试题广东省深圳市深圳外国语学校2024届高三上学期第一次调研数学试题(已下线)微专题09 隐零点问题(已下线)专题3 导数与函数的零点(方程的根)【练】
10 . 若函数
在
上单调递增,则a和b的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7a98b117e51c5fa3028888e37fd515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2024-01-25更新
|
904次组卷
|
5卷引用:浙江省温州市2023-2024学年高二上学期期末教学质量统一检测数学试题(A)