1 . 已知点
是圆
的动点,直线
上存在两点
,使得
恒成立,则线段
长度的最小值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e888af040ba6125443ccdf1f1aa0d902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6834ba6de422d87eedd475e419af10fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea8f7a80bdd8b95b88103efa57006d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2 . 定义在
上的幂函数
.
(1)求
的解析式;
(2)已知函数
,若关于
的方程
恰有两个实根
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d54e0619f9e71eb19b67200b8911c5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10356029baa6b16051b981471308a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f596b480c8326c15dbd72898d90c537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5c654afa70e0fa53240b284d202418.png)
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解题方法
3 . 已知函数
,若存在
满足
,且
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4244ef75d1f1ae0e0e6a7e96a593d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b21b263ad0664baffa35e3b38973d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5980421ce6ef4645da5eef55ad207987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1ab0e685b531494615932d85e284a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.5 | B.6 | C.7 | D.8 |
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4 . 已知函数
的部分图象如图所示,则下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/28a88e33-6e58-4e78-bd83-cd2e8832192c.png?resizew=135)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0ef9d537e1849ed448318247dce9f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/10/28a88e33-6e58-4e78-bd83-cd2e8832192c.png?resizew=135)
A.![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.![]() ![]() ![]() |
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解题方法
5 . 已知函数
,在
上单调递增,则实数
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f10eac3c12685dfa965e84991064223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.0 | D.3 |
您最近一年使用:0次
解题方法
6 . 已知函数
.若
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483796c965fccef2b613fa1b293d2d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9a102ee64dedb8c8f66dd862bf4443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
7 . 若方程
表示曲线C,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3d4ce1e61016c6b971f79d85ef9586.png)
A.若![]() |
B.若曲线C为双曲线,则![]() |
C.曲线C不可能是圆 |
D.若曲线C表示焦点在x轴上的椭圆,则![]() |
您最近一年使用:0次
名校
解题方法
8 . 已知数列
满足
,
,
.
(1)求证:数列
是等比数列,并求
的通项公式;
(2)记
,求证:对任意
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4309a9573d65ccb64ab69fefa50106.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f84a3e5e5f14d8f9f16bbd3b353a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fa34d5a86d929757c2bc3db1a51e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bc014a60531c08bcd710e01671d285.png)
您最近一年使用:0次
名校
9 . 在平行六面体
中,底面
是边长为2的正方形,侧棱
的长为3,且
,则
的长为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6c459662d5cc28d6b497b07f6456a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471927959af656b2ff02870388a062c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294a54c27a8d895190ce57b0f4cc222e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d92d9a29a3234e17db6fe0041c042f4.png)
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解题方法
10 . 已知椭圆
的右焦点为
,上顶点为
,直线上
上存在一点
满足
,则椭圆的离心率的取值范围为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24550b13dbecf7d86c7054250e987274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578faa3e92d60d4741a360898e46ce61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5bb9d2204b366da605e989c4153819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b56b32203ce83224e494c61d464288.png)
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