名校
解题方法
1 . 已知函数
.
(1)求不等式
的解集;
(2)若
,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276246854dd33691f6798db87faeea0b.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37dafb12565279285111a5948d835b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 已知正实数x,y满足
,则下列不等式成立的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-12-29更新
|
547次组卷
|
2卷引用:四川省成都石室中学2023-2024学年高一上学期期中考试数学试题
3 . 直线
过点
,则直线
与
轴正半轴、
轴正半轴围成三角形面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/170cf2cc33dae91cd546e15f4683330d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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4 . 已知
都是正数,且直线
与直线
平行,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee69fc5bd7de89b44913378caa38d52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909e6f55e045d730efd433ea4105ac6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547b5d4315e2130fa53173e53e28d0ff.png)
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5 . 设函数
.
(1)若
时,
恒成立,求
的取值范围.
(2)若实数a,b均为正数,且满足条件
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72c3164decaaad0798c17a880beeb98.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若实数a,b均为正数,且满足条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2845092c3b152b5e6a47879a7518e45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1cf1a1fe3fedb8f239dab815502c6dc.png)
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解题方法
6 . 已知不等式
的解集为
或
.
(1)求实数
、
的值;
(2)若
,
,
,并且
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e5b74496fa7094fd333199730b706c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da648ee55d60eb76c56cd747c30d40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5806497d3b5ec15d89eef8202d54d7a0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c83c336fe675092f68c192842d635b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b180ffd03aff4efda5c76dbfd5b13aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
7 . 我校艺术体育节将在11月29-12月2日进行,艺体节的主题为“魅力与和谐”,学校宣传部拟在一张矩形海报纸(记为矩形
,如图)上设计四个等高的宣传栏(栏面分别为两个等腰三角形和两个全等的直角三角形且
),宣传栏(图中阴影部分)的面积之和为
.为了美观,要求海报上所有水平方向和竖直方向的留空宽度均为
,设
.
![](https://img.xkw.com/dksih/QBM/2023/11/20/3372263549329408/3372308688183296/STEM/a360a90dc8fc41eea4eaec8002d4a4c0.png?resizew=160)
(1)当
时,求海报纸的面积;
(2)当
为多少时,可使海报纸面积最小(即矩形
的面积最小)?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f15bfd030c5d4b9cbe79cb76fd62ad9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7171acb1949bc69b96a82edf644765a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f69661563013a281608a016afeef7687.png)
![](https://img.xkw.com/dksih/QBM/2023/11/20/3372263549329408/3372308688183296/STEM/a360a90dc8fc41eea4eaec8002d4a4c0.png?resizew=160)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40924e7da720be1b6d80408fd626a66e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
8 . (1)已知
,
,若
,求
的最小值.
(2)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf913c92060a7bad4de1ee8c04d011e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef0134ea1669dcf9f1c623d1ace0ad.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e482dd69ac1cf7f06552fdf25a217c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764f465e2089adf4254ad999c8ef03a3.png)
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名校
解题方法
9 . 已知函数
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)解关于x的不等式
;
(2)若
的解集为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650f1997d6848622400a2c03f98e0400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)解关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27380616573e306aa5d96ed00333440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9c642d2895aa532c0a833ec0c6045f.png)
您最近一年使用:0次
2023-12-20更新
|
341次组卷
|
2卷引用:四川省成都市武侯区川大附中2023-2024学年高一上学期期中数学试题
解题方法
10 . 已知函数
.
(1)求不等式
的解集;
(2)若函数
满足
,若对任意
,不等式
恒成立,求实数
的最大值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb0b99a987ace63704fdc8ec5dbc7e0.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37badd4a593b4811efc3b03984af43e.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adeb806755d188539e2389ea680024da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db02c520989da5adce55d84410a644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4777fb5d74177a28f4a0fa9c599c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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