解题方法
1 . 已知函数
,
的零点分别是
与
.
(1)若
,解不等式
;
(2)已知
,
①证明:
;
②若
,
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3023e7cb9c12cd7789dd5babcbc81bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460fb23be742df604c9e3acbadb975d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97b49ac1c01655ddceb48cc71585f62.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d755a0a76e2102eb6e29db34df0903dd.png)
②若
![](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/123371927e0a2f94563eb7321039dfbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceddc345bfa05b7c0c61ec02470188a.png)
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解题方法
2 . 已知奇函数
的定义域为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acb74208dcbe73fd8cbd89bf86bd69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e23be533429387772591dc5124455e8.png)
A.0 | B.1 | C.2 | D.3 |
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3 . 有一组实验数据如表,则体现这组数据的最佳函数模型是( )
2 | 3 | 4 | 5 | 6 | |
1.40 | 2.56 | 5.31 | 11 | 21.30 |
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b9cb349fa686b6057bd1e3ed1cfae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c1f19fb2321a717c1e8c8927a93a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6ad1595b70b4ed251f0b46e68b4ca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfec00a7c1ce91dabbe786943f7f0673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 含有3个实数的集合可表示为
,又可表示为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e999b561583b4e422de4415d6e5b110.png)
_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40918974b3dd39f686bf1d6962490664.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac5ed38ebb5096affd6682970433ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e999b561583b4e422de4415d6e5b110.png)
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7 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca87295f36a2d30a1639592c4b5a7a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0389ca6c49a2af43452fe4cadce801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4198dc12226f85fae2348730c25ab6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知函数
是定义在
上的奇函数.
(1)求实数
的值;
(2)判断
在定义域上的单调性,并用单调性定义证明;
(3)
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cbc2ed4bad6431037602fc427e6756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5667bc1ea875422f618529aa5f254f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e9b1365d76a10c212db1c91c5f91f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
9 . 设集合
,
,
(1)若
,求
,
;
(2)若
中只有一个整数,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1aa2c6593b922adda24f698c682dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7259cb8656ee25e0cf139c5ef44bfa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3744e71abf4b43e128eabea9181b712.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9cf8dffa529bdb60c61af0d12c7e737.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e349af7d47125d7028ee57178e199da5.png)
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10 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fa7f541be676dee0b2f9ec7ad965db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1045c74528f68de164bcc78d6f0f135d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:河北省衡水市武强中学2023-2024学年高二下学期期末考试数学试题