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)
您最近一年使用:0次
名校
解题方法
2 . 若定义在
的函数
满足:对于给定的
,存在
,使得
成立,则称
具有性质
.
(1)函数
,
是否具有性质
,请说明理由;
(2)已知函数
具有性质
,求T的最大值;
(3)已知函数
的定义域为
,满足
,且
的图像是一条连续不断的曲线,问:是否存在正整数n,使得函数
具有性质
?若存在,求出这样的n的取值集合;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b006ca4156920323d4a6e5b824eb4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb03852bfba151574918a5ccdfa2eaeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c03be80f9a2db9ab33ff5505f9c22f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6be9a1c3d2ecfaf4aadfcd92c5f9204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facd8ef8a4f03cb439af27a89d25a35.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84c5adeb3bce246ebbe10df3ee61d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/716121901a339a5cfabd31a13562339e.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d7ce04b79ef6ae16d9d38288af2108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facd8ef8a4f03cb439af27a89d25a35.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b006ca4156920323d4a6e5b824eb4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499bc3e09a7b069e8eb33f4cc203c030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500965e9c4bf763d6f51c7abd2de309e.png)
您最近一年使用:0次
名校
3 . 若集合
,集合
,其中
,则称集合
是集合
的一个“
元子集”.若“
元子集”
中的元素
满足对任意
,恒有
,则称
为
的一个“个性独立子集”.已知集合
,集合
是
的一个“个性独立子集”.
(1)求所有满足条件的集合
的个数;
(2)若
且互不相等,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b7c647eb8e6be44689333e1a6f1f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ed4e9293f5066fe367cfa541afa11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d87fa699e2aca137f69e4ac0883dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4aecf0b7edfa826f73389322a52cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f2c01531dd639f0ad3da0098febbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effaffc8a4d01f865a79933d3c337060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求所有满足条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3fa353ea21d2dea55e32a354e3dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0736f73b81bec1c5d4efe968cfbe2a.png)
您最近一年使用:0次
名校
4 . 已知集合
,对于
,
,定义A与B的差为
,A与B之间的距离为
.
(1)直接写出
中元素的个数,并证明:任意
,有
;
(2)证明:任意
,有
是偶数;
(3)证明:
,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb64b23cfbc03c6ac0372a87bf81e9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d0135cb7ffda469b422df0aa1817d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c76f1774902da4c8da18791b5a35c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f960a435af66d6f53c96cf5d0d7ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e77ba8c90d21237670483bbcd8ac63b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a0663324985d2901305e58b066e763.png)
(2)证明:任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81345ca73b711411e665820b5672913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639d6bbfe09dcd8af9c993a086b25105.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5318f129bfbfca89f51c03144251ce79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac18fa333be06b2ba3711b0c7171913.png)
您最近一年使用:0次
名校
5 . 三角函数的定义是:在单位圆C:
中,作一过圆心的射线与单位圆交于点P,自x轴正半轴开始逆时针旋转到达该射线时转过的角大小为θ,则P点坐标为
,转动中扫过的圆心角为θ的扇形,由圆弧面积公式和弧度角的定义,可知面积
.类似地对于双曲三角函数有这样的定义:在单位双曲线E:
中,过原点作一射线交右支于点P,该射线和x轴及双曲线围成的曲边三角形面积是
,双曲角
,则P的坐标是
.其中,
称为双曲余弦函数,
称为双曲正弦函数同样,有类似定义双曲正切函数
双曲余切函数
且有如下关系式:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d279cc5e9f902480c9a0ea810cf9d3a.png)
,
的初等函数表达式.
(Ⅰ)双曲三角函数有如下和差公式,请任选其一进行证明:
①
;
②
;
(Ⅱ)①求函数
在R上的值域;
②若对
,关于x的方程
有解,求实数a的取值范围.
类似三角函数的反函数,试研究双曲三角函数的反函数artanhx,arcothx.
(2)①证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b450e870513b9cf6021b6416959224.png)
②已知
的级数展开式为
,写出
的级数展开式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b93ac1e1087ef8a7827e22983ab895f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33074bee68ff41ba4c6b675578f19957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c00da6d39ad0fae411836b0a26979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15cd370bd2337b78fe820b7b61438c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2dc9ac6460d3c72e915e93b9f16d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1fe4e3a61667cfe81973a300859f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a252d4a56c74a8829afb1fccbe09d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0961cbc097652b999cd4106c671e4cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d279cc5e9f902480c9a0ea810cf9d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
(Ⅰ)双曲三角函数有如下和差公式,请任选其一进行证明:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1079114cdde9367a22632b0165f1a1a8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3510bba38a7f232cc4d9e437e78f5b6a.png)
(Ⅱ)①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e154c56d574646a2a541a3fe70c6307b.png)
②若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f2372e3d0c3de8f5f0579312efe38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c47cddd4b31aeacfad8f81705b827.png)
类似三角函数的反函数,试研究双曲三角函数的反函数artanhx,arcothx.
(2)①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b450e870513b9cf6021b6416959224.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802ae3e64c0bb802cc83bf3cf81bfe49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1bbb717893d3adb6ce58b3a99bc257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0593e23740ebd0cd068a2eadf059e3.png)
您最近一年使用:0次
解题方法
6 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b676538aa3f0e39a6fe04691eb816b7c.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.不等式![]() ![]() |
您最近一年使用:0次
7 . 已知
,给出下列命题:①
的图象关于点
对称;②
的值域为
;③
在区间
上有33个零点;④若方程
在区间
有4个不同的解
,其中
,则
的取值范围是
.其中所有正确命题的序号为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129be9bb55128c679bbc588fa7e63f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8c5671c7a231e69641186f554755f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378c3d729d1d0bf2b2c0ece2da407038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf339f342957d390daf5be25fe933ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f62acf7b2e380cd659f33f503a2a74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004f0cecc857b24d535272fe84ecd19e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d138ce9e3abdd755f24834eadb10eb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7d6dda12b3f1ea472296bef3c10669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f13113ce731797a3dc018c82041ce3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0652d0d3e33b123bea077cb6573c5e6f.png)
您最近一年使用:0次
名校
8 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在
个不同的实数
,使得
(其中
),则称
为
的“
重覆盖函数”.
(1)试判断
是否为
的“2重覆盖函数”?请说明理由;
(2)若
,为
,的“2重覆盖函数”,求实数
的取值范围;
(3)函数
表示不超过
的最大整数,如
.若
为
的“2024重覆盖函数”请直接写出正实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d5df7922a4e98e8e07bf418dd48a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d1a18f254577a0ce74ceb27364b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b96b909824873058aebdaa54f6c21ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a264b8541eddc8ae86058de027d1a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f246e5b05b68bb9fdeb12a319aa7136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa88c20e58953bba4ed04d3ce419df95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ca781ffd5d55cc9b7dd551879ce65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4987dca9120f6a58139fd3e412ed77c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a899e901b141a0a6d56e3387ecf9f047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-29更新
|
236次组卷
|
2卷引用:湖北省鄂西南三校2023-2024学年高二下学期三月联考数学试卷
名校
解题方法
9 . 已知
满足三个条件,其中两个条件分别是:
,
.若这样的
恰好有2个,则第三个条件可以是_________ (选出所有符合要求的答案的序号)
①
,②
,③
是等腰三角形,④
是直角三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1cac92e1b66c7c34f5e91d079655048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36ec31cfd615abfbee3ed2f4a1d8883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d0a801922c34467a5d058ed57d664e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
名校
10 . 若函数
(其中
)在区间
上恰有4个零点,则a的取值范围为___________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aace095eebc2d644e1e1c4bb088c1110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab90f84a9b6ec1334ce6fc12495ec218.png)
您最近一年使用:0次
2024-03-25更新
|
1569次组卷
|
3卷引用:天津和平区2024届高三一模数学试题