名校
1 . 已知集合
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd83907b1f4a03ab969fbdda6cf908d3.png)
(1)当
时,求
.
(2)是否存在实数
,使得
,说明你的理由;
(3)记
若
中恰好有3个元素,求所有满足条件的实数
的值.(直接写出答案即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/857f9714cce576c2e77b925edb9c9621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd83907b1f4a03ab969fbdda6cf908d3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d322409dc07251b75e28050217c0561.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5d01a8873720061d3f93cd6f1b79e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709a1f33195ab62f2da488b27a219c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
2 . 已知
,且
,函数
,
在
上是单调减函数,且满足下列三个条件中的两个:①函数
为奇函数;②
;③
.
(1)从中选择的两个条件的序号为_______,依所选择的条件求得
______,
_______(不需要过程,直接将结果写在答题卡上即可)
(2)在(1)的情况下,若方程
在
上有且只有一个实根,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7d388df8a41777cbc3755fbd80efd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7926703c19e89a7438753101df731738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e88c844860c1d1eaeb80660679ca928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a1e4572e907ff8abb63b998d6d5c1e.png)
(1)从中选择的两个条件的序号为_______,依所选择的条件求得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
(2)在(1)的情况下,若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6735e3aa27d0ba04ec310fb4bfd9ceb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
您最近一年使用:0次
2023-01-05更新
|
243次组卷
|
2卷引用:北京十一实验中学2022-2023学年高一上学期期末教与学诊断数学试题
名校
解题方法
3 . 已知函数
.
(1)在直角坐标系
下,画出函数
的草图(用铅笔作图);
(2)写出函数
的单调区间;
(3)若关于
方程
有
个解,求
的取值范围(直接写出答案即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5399eee71383eec4ae5b92b817ee430b.png)
(1)在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb101c5df08aa35ae24a6416840b199b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
4 . 利用周期知识解答下列问题:
(1)定义域为
的函数
同时满足以下三条性质:
①存在
,使得
;
②对于任意
,有
;
③
不是单调函数,但是它图象连续不断,
写出满足上述三个性质的一个函数
,则
______(不必说明理由)
(2)说明:请在(i)、(ii)问中选择一问解答即可,两问都作答的按选择(i)计分.
(i)求
的最小正周期并说明理由.
(ii)求证:
不是周期函数.
(1)定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07ad90ca228230b03f12eb48ee0c1d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c01f065ba99f4c6273150c4a4eda74.png)
②对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af189539e23bce4efa3fb48bea7b6e95.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
写出满足上述三个性质的一个函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba99a5c5661eedaef4b36ade1a7c5c5.png)
(2)说明:请在(i)、(ii)问中选择一问解答即可,两问都作答的按选择(i)计分.
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e19711f97dadb766a30c6746ceace4f.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722ad2058c44092bd4c329117e5ccea6.png)
您最近一年使用:0次
名校
解题方法
5 . 对于非负整数集合
(非空),若对任意
,或者
,或者
,则称
为一个好集合.以下记
为
的元素个数.
(1)给出所有的元素均小于
的好集合.(给出结论即可)
(2)求出所有满足
的好集合.(同时说明理由)
(3)若好集合
满足
,求证:
中存在元素
,使得
中所有元素均为
的整数倍.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36aecba41f6f5ff0d46a29dccaaf01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b8e5872f45d4b878b0119997cb5bae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84734fbba70c0b45045fabf8090f810b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911cdb689ca80557ce076cb49b3ee498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)给出所有的元素均小于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)求出所有满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7a6d4b773d984df6fd1e0dce3adfb9.png)
(3)若好集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fc21f14cb5d8d28f498d35606477ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
6 . 已知函数
,
.
(1)当
时,求
的解集;
(2)求使
的
的取值范围;
(3)写出“函数
在
上的图象在
轴上方”的一个充分条件.(直接写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b14ddea7512b395c31028251c1d2323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(2)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)写出“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4cf16e39bff4aa2d482c90411d5ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2020-03-02更新
|
442次组卷
|
2卷引用:北京市大兴区2019-2020学年高二第一学期期中考试数学试题
名校
7 . 已知函数
.
(1)用函数单调性的定义证明函数
在区间
上是增函数;
(2)求函数
在区间
上的最大值和最小值;(第( 2 )小题直接写出答案即可 )
(3)若对任意
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1510639120a1883e66f13794a9df9179.png)
(1)用函数单调性的定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e390f45a8413c7b10023ea0d6543ca0.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f20e9fee5cd966d902e0ae35538d24e5.png)
您最近一年使用:0次
2019-12-08更新
|
316次组卷
|
2卷引用:北京市第二十二中学2019-2020学年高一上学期期中数学试题
名校
解题方法
8 . 已知函数
的定义域为
,若存在实数
,使得对于任意
都存在
满足
,则称函数
为“自均值函数”,其中
称为
的“自均值数”.
(1)判断定义域为
的三个函数
,
,
是否为“自均值函数”,给出判断即可,不需说明理由;
(2)判断函数
是否为“自均值函数”,并说明理由;
(3)若函数
为”自均值函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9f57537b1a7ca7e4eed38a922ac707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)判断定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b78b98443d32512ddcfe86aefd507db.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543634891d61ea51e686c850533f24ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
2024-03-25更新
|
276次组卷
|
2卷引用:北京市海淀区中央民族大学附属中学2023-2024学年高一下学期期中练习数学试卷
名校
9 . 已知函数
.
(1)判断函数的奇偶性,并说明理由;
(2)求证:函数
在
上单调递减;
(3)写出函数
,
的最值,及取到最值时对应的x值(不需说明理由,直接写出结论即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5effb3053cf609f59178641cd48167.png)
(1)判断函数的奇偶性,并说明理由;
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ed49839c4dc0b033431d88a4c1f94.png)
(3)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5effb3053cf609f59178641cd48167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/695372ac0e0423f72bf85c8bbb474580.png)
您最近一年使用:0次
名校
10 . 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)
您最近一年使用:0次