名校
1 . 函数
.
(1)若
的定义域为
,求实数a的取值范围;
(2)当
时,
为定义域为
的奇函数,且
时,
,
①求
的解析式
②若关于x的方程
恒有两个不同的实数根,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a1bbd20e3530f75fc3c52a5648288f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790b68061b533ed19f0c594314fc4dc8.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f432ff1145d529f680b88b8f767c5a.png)
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2 . 我们称各项均不相等的正项数列
为“冒泡数列”,对任意冒泡数列,我们按如下步骤进行操作,称为“冒泡操作”
比较
的大小,若
,则交换
的位置;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,若
,再交换
;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,
,直到比较得到
时或者
调整位置至首位时停止比较和交换位置,并进行下一步;
设前述所有步骤后数列变为
,比较
的大小,若
,则交换
的位置,再继续比较
的大小,…,直到比较得到
或者
调整位置至首位时结束操作.
(1)请对数列
5,3,2,9,7作冒泡操作,可表示为
请写出操作结束后得到的数列,并计算交换位置的次数.
(2)对于某个
项冒泡数列
当其完成冒泡操作时的总的交换位置的次数称为其“交换复杂度”,记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a802b2e8db56dfb2f367fbbd9c4fe0f.png)
(i)求
的最小值和最大值;
(ii)对于某个
项冒泡数列
及其各项全排列产生的所有不同数列,其交换复杂度的平均数记为
,求
的通项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8e9680996fdd9e3a40f62d810e92e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa559d2ca921738d0c6c51f3a036880.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ade3a1d01605706801e238726e55fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0158862238e250d2a2598b7d4ecd148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0cfe1386cf3dae99d19bf57895c9f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a25a0b38f47e113fd4dd76832de690a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fee2a3f8c67509707271a3f266a8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8784badc8cc600bef381da22d1c628d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fee2a3f8c67509707271a3f266a8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0525db7ca68c21dfe7a1c4b543b4bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9017d3641140e0692048ddbab24d1d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0525db7ca68c21dfe7a1c4b543b4bee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5356eacad97dae1c7e865903171245ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee15a08d7dc7c77ea81607b1f214c092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebefe3e26bef1c8422bfe5a472e0d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bc971d069730aa97e8734fc884e3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebefe3e26bef1c8422bfe5a472e0d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240e1ed0392e64705738776ff88b1623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0d398803d6a57b99fbb7994edc767b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed3a0a9f46932f86611d64711d81c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cace8ff9678eca7c3386f280c4ed8c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a67cfcf87e8b88246d7c8e101041bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0be03feff9bfb3b2f45a34b6fc2578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a67cfcf87e8b88246d7c8e101041bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d151f7e01f394c4547e8065de1adb689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5aeba46b164eea610a02251cdbfba03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)请对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/569675dd7b2aca2732324f4bea5c02e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acd875285006bca9792d6ffbea60191.png)
(2)对于某个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be66b629b36c5fe55ff234ad59bffff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a802b2e8db56dfb2f367fbbd9c4fe0f.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94511620a0ee01ebcc8ac2f3a47ac87d.png)
(ii)对于某个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de53713b20a2f956c2590ce71fb69c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de53713b20a2f956c2590ce71fb69c37.png)
您最近一年使用:0次
名校
3 . 已知曲线
在点
处的切线为
.
(1)求直线
的方程;
(2)证明:除点
外,曲线
在直线
的下方;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1026c00ff9d78946b4984d09de77995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f84134092f31767ff9f7e8200a79fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:除点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa83d5be9b28fcfce25c9bfca0d3d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab873c4173a3992c043fbf32cab4d8c.png)
您最近一年使用:0次
2024-04-26更新
|
1289次组卷
|
4卷引用:湖南省永州市第一中学2023-2024学年高二下学期6月月考数学试题
4 . 若函数
,且
的图象与直线
没有交点,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ef270c3ca8e2600fd00503bd331010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a0e656a2de8d47b9001cc32b1316eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684b2343643fdc021e07e2a6f393daf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
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名校
解题方法
6 . 已知双曲线
的右顶点
,它的一条渐近线的倾斜角为
.
(1)求双曲线
的方程;
(2)过点
作直线
交双曲线
于
,
两点(不与点
重合),求证:
;
(3)若过双曲线
上一点
作直线与两条渐近线相交,交点为
,
,且分别在第一象限和第四象限,若
,
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a62c9695f5a1691c5fe8724fa764b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ab813ed1a71746f27c49cc074bb6e8a.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a10e9c078acc907693e01bab8a29c37.png)
(3)若过双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184459410405a907798a625760c0d717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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名校
7 . 定义:在平面直角坐标系中,设
,
,那么称
为P,Q两点的“曼哈顿距离”.
(1)若点
,求到点O的“曼哈顿距离”为1的点的轨迹;
(2)若点E是直线l:
上的动点,点F是圆C:
上的动点,求
的最小值;
(3)若点M是函数
图象上一动点,其中e是自然对数的底数.点
是平面中任意一点,
的最大值为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea37e25ba5e11e5e2c428996f74e5a.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
(2)若点E是直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340e9eac0866ece3535f098929d2be4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fb5f15e33b3605da059678aa95ab81.png)
(3)若点M是函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a4bab250a1cd23c58ec0211be1077ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6134983a8decef61d715c3eedb9f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d7224242ab75080dfb394a39ebf7f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f795ec3610e5448ce6e7b55a72f667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f795ec3610e5448ce6e7b55a72f667.png)
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名校
8 . 如图,在棱长为2的正方体
中,已知
,
,
分别是棱
,
,
的中点,点
满足
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f36a6370254d829ad191cb5727ea32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79296cd4046a71e163a8f3e647a176ae.png)
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-11更新
|
1123次组卷
|
5卷引用:湖南省长沙市长郡中学2023-2024学年高一下学期4月选科适应性检测数学试题
名校
解题方法
9 . 已知函数
图象如图1所示,A,B分别为图象的最高点和最低点,过A,B作x轴的垂线,分别交x轴于
,点C为该部分图象与x轴的交点,
与y轴的交点为
,此时
.将绘有该图象的纸片沿x轴折成
的二面角
,如图2所示,折叠后
,则下列四个结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888dcf2660bb3803649ba8966129a77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77993759b8615ef0b42cb56ef027ff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/312f91b78abb3c06d747589ffa9209d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d7e95f2c5bf403b912183e162887b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068882b775725e852b7817740705ae38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b4836786aca156de325464ea2ecd9.png)
A.![]() |
B.![]() ![]() |
C.在图2中,![]() ![]() ![]() |
D.在图2中,若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-04-10更新
|
835次组卷
|
2卷引用:湖南省长沙市第一中学2023-2024学年高二下学期第一次阶段性检测数学试题
名校
10 . 已知函数
.
(1)讨论
的单调性;
(2)若
恒成立,求
的取值集合;
(3)若存在
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fb6e0db82c11dbf6d4a022b12dcbd4.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb948b7736245b30c44ef9270da0f88f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a78f37a26bad9bcd4165fedc05ce56c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-04-02更新
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5卷引用:湖南省衡阳县三校联考2023-2024学年高二下学期4月月考数学试题