名校
1 . 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
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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
2 . 已知函数
的定义域为
,且满足
.当
时,
.若方程
(
,
为自然对数的底数)的一个根为
,且
为不等式
的一个解,则实数
的取值可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe8b59d999909f9e584516c6daee8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee69a7e140ba1fcd975e15480b14ec55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d36d57e4be1b355a0afce95824a72bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb04bf1be2137245cf18784ce85454a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.0 | B.![]() | C.![]() | D.![]() |
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名校
3 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cba1effecd2347918494e7f07ea6236.png)
(1)当
时,求
的单调性;
(2)求证:
有唯一实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cba1effecd2347918494e7f07ea6236.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
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解题方法
4 . 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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5 . 已知
,其中
.
(1)当
时,分别求
和
的
的单调性;
(2)求证:当
时,
有唯一实数解
;
(3)若对任意的
,
都有
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a0328280d3360590b33257ae600eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(3)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
您最近一年使用:0次
2022-01-26更新
|
1102次组卷
|
7卷引用:江苏省南京市第二十九中学2022-2023学年高二下学期3月月考数学试题
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