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1 . (1)解不等式组:
(2)先化简,再求值:(
-
)÷
,其中x=
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731bc155992954c7899fb0669576e594.png)
(2)先化简,再求值:(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60b122e651b49f676e07bd8c815006f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76241e782e13eeee7c187507778aecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b05e238548dc202137a63d8b20ff277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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2 . (1)计算:
.
(2)解不等式组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37a3bda6b01e0ba1ae371376e744e14.png)
(2)解不等式组:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ad7595a8ee68167572656178331c02.png)
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3 . (1)计算:
;
(2)先化简,后求值:
,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2393fbd54f9528459f5f5cbe0290c1a.png)
(2)先化简,后求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8998c5f571a64b637a2366ecb19a37e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
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解题方法
4 . 记
,其中
,例如
.
(1)若
,求
的取值集合;
(2)解关于
的不等式
;
(3)已知对任意正整数
,实数
满足
,记
,其中n为正整数,若
且
,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4530cd47a73dd9a1b2d89a0b5daeec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23401fbb87375f9022c1e118a796f404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbea4bf2a650b088fddb1c328a215eb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d62b27b74240d7a80d7bbaafe4c39b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487c82925e104d62153dbb7753ff9c86.png)
(3)已知对任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce67db3a873de832a685b0324b95b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b091b775b7a4c75127570108d0edb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c16f21fb7ef4b9b98a81cdad840098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb4e491019643f3f86bd011dcbd7139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2022-09-06更新
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457次组卷
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4卷引用:上海市建平中学2021-2022学年高一上学期期中数学试题
上海市建平中学2021-2022学年高一上学期期中数学试题(已下线)期中模拟预测卷02(测试范围:前三章)-2022-2023学年高一数学上学期期中期末考点大串讲(沪教版2020必修第一册)内蒙古自治区赤峰市红山区2022-2023学年高一上学期期末数学试题(已下线)第二章 等式与不等式(压轴必刷30题7种题型专项训练)-【满分全攻略】(沪教版2020必修第一册)
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解题方法
5 . 取整函数最早出现在著名科学家阿兰•图灵(AlanTuring)在20世纪30年代提出的图灵机理论中.图灵机是一种理论上的计算模型,其中操作包括整数运算和简单逻辑判断.由于图灵机需要进行整数计算,因此取整函数成为了必需的工具之一.现代数学中,常用符号
表示为不超过
的最大整数,如
,现有函数
在区间
上恰好有三个不相等的实数解,则
的取值范围是( )
![](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/216a99672219e0c25fe670d654f954be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8fa0eac06d206de0fae577ea97a792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc7bc07dde43da45e75bb38793257f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-26更新
|
141次组卷
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2卷引用:浙江省台金七校联盟2023-2024学年高一上学期11月期中联考数学试题
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6 . (1)化简:
.
(2)求值:
.
(3)设
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9425b2d567b729467fec9498c183e32d.png)
(2)求值:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349678bf311bf77582444d12907a4428.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5aca7f0097fc0562c40375ce6756d56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bb6f1d6a053b78c221624885791f66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2893bd2a2299d8180f45494ba593d1.png)
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解题方法
7 . 函数
,
(1)解关于
的不等式
;
(2)若
,
①若
,求证
;
②画出
的图象.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5ee992e4d7904e80e246a908fe9051.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e342b2932a0414a3221e961c0e116aa.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764f981a79d9850e2fd2afb79940da50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e297f6897dec36236986df208904d9.png)
②画出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
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8 . 设
的定义域为
,若
,都有
,则称函数
为“H函数”.
(1)若
在
上单调递增,证明
是“H函数”;
(2)已知函数
.
①证明
是
上的奇函数,并判断
是否为“H函数”(无需证明);
②解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625151f40f341575c1a71992e485188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2bfd103090863fbcc1bd10618cff0c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0c77ba1db113cb10f711a0a42325bc.png)
①证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d3ca700dbdfefffcc21eb9eb9dc22a8.png)
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9 . 定义在
上的函数
满足
,且
,其中
且
.
(1)求实数
的值;
(2)已知:当
时,函数
的单调递增区间为
;当
时,函数
的单调递增区间为
;解关于
的不等式
;
(3)若函数
,
.是否存在实数
,使得函数
的最小值为
.若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c0f05773123ba547d3c3601f846f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4dee8772c3677042a63e7c3d098d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a887738d524cc365eb6befcc6f8576bc.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)已知:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e58768fc0df02f60aa54d00fe063c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed4a706b9ce4cdad66280c6e74862b4.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f7bf77d0f4691796d3eaaeff6852401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4072465b5db70c85dea5ec96cc468029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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10 . 对数
中的实数
的取值范围与下列哪个不等式的解相同( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22cbe3b3f024664dcd8c02b25c6a24c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-11-15更新
|
307次组卷
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4卷引用:上海市松江二中2022-2023学年高一上学期期中数学试题
上海市松江二中2022-2023学年高一上学期期中数学试题上海市七宝中学浦江分校2023-2024学年高一上学期期中考试数学试题(已下线)1.对数的概念-同步精品课堂(北师大版2019必修第一册)(已下线)【第三练】4.3.1对数的概念+4.3.2对数的运算【第三练】上好三课,做好三套题,高中数学素养晋级之路