1 . 设
是定义在R上的函数,其导函数为
.
(1)若函数
,求
的值;
(2)若
是奇函数,当
时,恒有
,求不等式
的解集;
(3)若对于任意的实数
都有
,且
,若关于
的不等式
的解集中恰有唯一的一个整数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8077229346193d3fb9624d83279c0f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383acb6637f314601906b2b617c823bc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e746182b4fd3a7bdbd07b937fd5af444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/867e9e947736b4c2f09430ecc84467ff.png)
(3)若对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4367d37b1b82c37f6660c6ab8272018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c9a7ed0961f8977a21dab37aab396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4823e3917929f102d99a8db8e2d569f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
2 . 若关于
的不等式
的解集中恰有2个整数,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f5c44632b73062fffc727e09d1e8a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-06-18更新
|
546次组卷
|
4卷引用:四川省成都市蓉城名校联盟2022-2023学年高二下学期期中联考数学文科试题
名校
解题方法
3 . 设常数
.在棱长为1的正方体
中,点
满足
,点
分别为棱
上的动点(均不与顶点重合),且满足
,记
.以
为原点,分别以
的方向为
轴的正方向,建立如图空间直角坐标系
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/e06e4e4f-445b-442f-8e80-1e0f640affc9.png?resizew=217)
(1)用
和
表示点
的坐标;
(2)设
,若
,求常数
的值;
(3)记
到平面
的距离为
.求证:若关于
的方程
在
上恰有两个不同的解,则这两个解中至少有一个大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a91c73ae980263c97742283b6b5852a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea77ba313fcc751481ac1ca214df3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e85b55b6ad43be1a03fc637e1d3429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651066b6919cab279373a8a1e1130839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68873c59a21b0cd408cdf2b47d51096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/e06e4e4f-445b-442f-8e80-1e0f640affc9.png?resizew=217)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15b268af571f9ecb37a864a08862814.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262b77e692c60e3c6b6afb610e8fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28b88046022376b082b8a45c04577c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a90170d7ef5ff6d1d63517c166f7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a19e72906b84a1cb049167afdebdce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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解题方法
4 . 已知函数
.
(1)当
时,求方程
的实数解;
(2)若对任意
,
恒成立,求实数
的取值范围;
(3)若存在两个不相等的正实数
,
,满足
,试比较
、2、
这三个数的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69141912718ee2eb9e3b5b20076a2f2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0097b2a40fd339906bb03607246d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若存在两个不相等的正实数
![](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/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
您最近一年使用:0次