1 . 已知抛物线
的焦点为
,在
轴上的截距为正数的直线
与
交于
两点,直线
与
的另一个交点为
.
(1)若
,求
;
(2)过点
作
的切线
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,则当
的面积取得最小值时,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a68ce9569af419362238f6f24f5a5f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc094d6bccc3b13a496b9c3a423f737.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:河南省濮阳市2024届高三下学期第一次模拟考试数学试题
名校
2 . 已知函数
.
(1)若
,讨论
的零点个数;
(2)若
是函数
(
为
的导函数)的两个不同的零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a441ed40dca1a0f8c5ed0253d1ca300.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab42358409a44ea7a55fe532fe66ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b550cb121a3346f8d46b7f7ee2117d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380beb181ed0a48cc486131bba4a4c46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d106beb9c7a567f35e7f3407f41c963c.png)
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3 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,若
分别为
的极大值点和极小值点,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682f847b99736449dbed71d1b2925f0a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068ff25c767fcbe6fe596d996031eed1.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882b660047bb6ded500cedba57958e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaeb1e529e152749236dbc8d9385f143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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4 . 已知函数
.
(1)讨论
的单调性;
(2)若a>0,记
为
的零点,
.
①证明:
;
②探究
与
的大小关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133bb541dbb30d83cd28f5c8f0dcec76.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若a>0,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a52e87ce5b62171eaedaed75a2b5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef07479887c8a2c1c26000f0b9847092.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa308d7f4f68a95753272c9a039d686.png)
②探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a52e87ce5b62171eaedaed75a2b5db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c16d0f58b8b7c2c11dfdc01197063cf.png)
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2024-01-26更新
|
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2卷引用:河南省郑州市宇华实验学校2024届高三下学期开学摸底考试数学试题
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5 . 已知球
的半径为2,点
是球
表面上的定点,且
,
,点
是球
表面上的动点,满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6a21e67e232d5db608299f0bc364ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ffe9de3a135dac9e970edd2bc979b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224dc2a6139f056e1a219acc648eae6a.png)
A.有且仅有一个点![]() ![]() | B.点![]() ![]() ![]() |
C.存在点![]() ![]() ![]() | D.![]() ![]() |
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解题方法
6 . 已知A,B是椭圆
的左右顶点,
是双曲线
在第一象限上的一点,直线
分别交椭圆于另外的点
.若直线MN过椭圆右焦点F,且
,则椭圆的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad57e3727b7bbd795b05332fbf9649e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7489045105c8881adfa39bb05bf7d98.png)
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4卷引用:河南省南阳市第一中学校2023-2024学年高二下学期开学考试数学试题
河南省南阳市第一中学校2023-2024学年高二下学期开学考试数学试题辽宁省沈阳市东北育才学校2023-2024学年高二上学期第二次月考数学试题广东省广州市铁一中学2024届高三上学期第二次调研数学试题(已下线)专题4 求圆锥曲线的离心率(高三压轴小题大全)【练】
7 .
有两个零点
.
(1)
时,求
的范围;
(2)
且
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36963e5a7af852facd9a90a621cf53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7828efd05480bda612eef0c19727df89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e653f112568c8203f73105f38793de.png)
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解题方法
8 . 已知函数
(
为自然对数的底数),则函数
的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b6ee7feb8a7df4da66b2323bebb441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80be487817e3de0539863c0f4a448e12.png)
A.1 | B.3 | C.5 | D.7 |
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河南省2024届高三上学期起点考试数学试题河南省洛阳市洛宁县第一高级中学2023-2024学年高三上学期第二次月考数学试题(已下线)第四章 导数与函数的零点 专题三 复合函数零点问题 微点1 复合函数零点问题(一)(已下线)模块二 大招18 复合方程的实数根问题
名校
9 . 已知函数
.
(1)求曲线
在
处的切线方程;
(2)记函数
,设
是函数
的两个极值点,若
,且
恒成立,求实数m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b3a22b28217af79ce27c83b2a57588.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6ff1f6422eb3a03fa5107b2d56b061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebf7dd44e24f45150d01af41948e761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead3e7f90f220e4e3574a3bf29b91e95.png)
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河南省南阳市第一中学校2023-2024学年高三上学期开学考试数学试题广东省珠海市斗门区第一中学2022-2023学年高二下学期6月阶段考数学试题(已下线)第六章 导数与不等式恒成立问题 专题九 双变量不等式恒成立问题 微点3 双变量不等式恒成立问题之换元法
10 . 已知实数
,函数
,
.若方程
在
上有且仅有4个实数根,则实数
的取值范围是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91af7006414826041eada8d63b3afcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adee3b3a1d2b4df4f0733cc6e23bb47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8bfb563f79688d136e0cb958b5153c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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