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1 . 已知函数
.
(1)若
,判断
在
上的单调性;
(2)若关于
的不等式
在
上恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cb8c64e4c081d41835cc9c5b2107623.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd82b5223c2a708c1729db2a3750990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e58768fc0df02f60aa54d00fe063c52.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb505382220fe1021bdc15051e014025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-19更新
|
425次组卷
|
4卷引用:安徽省池州市贵池区池州市第一中学2022-2023学年高二下学期6月月考数学试题
名校
解题方法
2 . 已知直线
过定点
,双曲线
过点
,且
的一条渐近线方程为
.
(1)求点
的坐标和
的方程;
(2)若直线
与
交于
,
两点,试探究:直线
,
的斜率之和是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83962152f2c4b718e0ed64d9902392ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1646a3e70ab060266aace42a0a6be100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
您最近一年使用:0次
2023-06-19更新
|
553次组卷
|
5卷引用:安徽省池州市贵池区池州市第一中学2022-2023学年高二下学期6月月考数学试题
安徽省池州市贵池区池州市第一中学2022-2023学年高二下学期6月月考数学试题1号卷·A10联盟高二年级(2021级)下学期6月学情调研考试数学试题安徽省十校联盟2022-2023学年高二下学期6月联考数学试题(已下线)第22讲 双曲线的简单几何性质9种常见考法归类(2)(已下线)专题3.9 圆锥曲线中的定点、定值、定直线问题大题专项训练【九大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)
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3 . 已知函数
和
有相同的最大值
.
(1)求
;
(2)证明:存在直线
,其与两条曲线
和
共有三个不同的交点,并且从左到右的三个交点的横坐标成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f7bc44601553dd5e49f2e599579db3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8999865b50a6a1f4306c6ec8be5534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)证明:存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
4 . 已知双曲线
过点
,且焦距为
.
(1)求
的方程;
(2)已知过点
的动直线
交
的右支于
两点,
为线段
上的一点,且满足
,证明:点
总在某定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cda9ce6d633bc1f3a249fb0fc458a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491f6873b3f0ee29a8ce680eb25c1116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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5 . 已知实数
满足
,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db561d78103d9a363b1907947db7c8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d65341447f95880aef2ec15169a86aa.png)
您最近一年使用:0次
名校
解题方法
6 . 如图,正四棱柱
中,
,动点
满足
,且
.则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/19/e403700e-5406-4497-a85b-a4ba94c21cff.png?resizew=139)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f21c7c194c5bc2986a21fd441c81495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a871156caa5d7222c7944afecf5f9ea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1c15263cbb460891a4af6a9c693060.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/19/e403700e-5406-4497-a85b-a4ba94c21cff.png?resizew=139)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.若直线![]() ![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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解题方法
7 . 已知函数
的定义域为
,
为
的导函数,
,
,若
为偶函数,则以下四个命题:①
;②
;③
;④
中一定成立的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9946f4261da1b690dc271928a11276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff696ebb3a753b846b0522241402a42f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62212f9eb57eaee72aaf5b0f747e9d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5750e5b498cd76b6d0c03e45201a351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748f743823d06ca8e38a40481504b18e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/429ccc9ad3f0331c69f8e2a052e3ff97.png)
A.1 | B.2 | C.3 | D.4 |
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解题方法
8 .
间的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeaeeb716b2595a374e9c2d844223f5a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
9 . 已知椭圆C过点
,
;过原点且不与坐标轴垂直的直线l与椭圆C交于M,N两点.
(1)求椭圆C的标准方程;
(2)记椭圆C的右焦点为F,分别延长MF,NF交椭圆C于M',N'两点,探究:直线M'N'是否过定点,若是,求出定点坐标;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0826e47a8eef4b2c48b851471d66bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b468bcd5fc751db799753a3235cee19.png)
(1)求椭圆C的标准方程;
(2)记椭圆C的右焦点为F,分别延长MF,NF交椭圆C于M',N'两点,探究:直线M'N'是否过定点,若是,求出定点坐标;若不是,请说明理由.
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10 . 已知函数
.
(1)若函数
有2个零点,求实数m的取值范围;
(2)若m=0,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b6a51a367cba90ef6f4eaad966fff6.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若m=0,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292529e413f52e7ea60be53c5b908cb8.png)
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