1 . 已知函数
.
(1)若曲线
在
处的切线经过坐标原点,求a的值
(2)若方程
恰有2个不同的实数根,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c0be0f5a112a7d38a2ccb7d4e922c4.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df18da1ecd1a83afc4544ee71f00c56b.png)
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5卷引用:陕西省商洛市多校2023-2024学年高三上学期11月联考数学(理科)试题
2 . 已知抛物线
的焦点为
,直线
过点
且与抛物线
交于
,
两点,直线
过点
且与抛物线
交于
,
两点.
(1)若点
,且
的面积为
,求直线
的斜率;
(2)若点
,
在第一象限,直线
过点
,比较
与
的大小关系,并说明理由.
![](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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241ce9bd28046ce9b90f43b391132884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588c3822b7812e711b4ad86647b15dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eab8a432f42f6cbf5a5b2ee07d4e4eb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecfa5de2acaec4133be44dc9c8c62f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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3卷引用:华大新高考联盟2023-2024学年高三上学期11月教学质量测评理科数学试题
3 . 已知函数
.
(1)若
,求
的图象在点
处的切线方程;
(2)若
在区间
上单调递增,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f66891d307bae4eb784b212ce49595.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b680f82d5ee3804b1fa103044347956c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31d4e0c338a1027f89e8b9179c26e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-11-01更新
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3卷引用:2024届高三上学期10月大联考(全国乙卷)理科数学试题
解题方法
4 . 已知函数
,
.
(1)求
的极值;
(2)证明:当
时,
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923fcc6830f02925f594edcb9fcc90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bcf1135449e1c9bb97f6927aa55b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cd1568daf759620e6842d75d88d558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
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2023-09-19更新
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2卷引用:陕西省西安市第八十三中学等校2023届高三二轮复习联考(一)文科数学试题
5 . 椭圆
的离心率是
,点
是椭圆
上一点,过点
的动直线
与椭圆相交于
两点.
(1)求椭圆
的方程;
(2)求
面积的最大值;
(3)在平面直角坐标系
中,是否存在与点
不同的定点
,使
恒成立?存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d9b4a5f5334c153ddbefc763d8939ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(3)在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a97e38fffbca986dee7e2cb28bb794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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9卷引用:陕西省西安市长安区第一中学2024届高三上学期第五次教学质量检测数学(理)试题
陕西省西安市长安区第一中学2024届高三上学期第五次教学质量检测数学(理)试题四川省仁寿第一中学校南校区2022-2023学年高二上学期期末理科数学试题(已下线)3.1.2 椭圆的简单的几何性质(AB分层训练)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)高二上学期期中复习【第三章 圆锥曲线的方程】十二大题型归纳(拔尖篇)-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)黑龙江省牡丹江市第一高级中学2023-2024学年高二上学期11月期中考试数学试题(已下线)上海市徐汇中学2023-2024学年高三上学期期中考试数学试题变式题16-21(已下线)第三章 圆锥曲线的方程(压轴题专练)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)专题06 椭圆的压轴题(6类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)(已下线)专题突破卷23 圆锥曲线大题归类
名校
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf266c400ec9f20afcdb1c76a62c6c8.png)
(1)若
,讨论
的单调性.
(2)当
时,都有
成立,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf266c400ec9f20afcdb1c76a62c6c8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64cd4438dd55cf77a66bc3d7778e0670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a7ec599d83020b3407c80466f6b43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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|
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7卷引用:陕西省渭南市合阳县合阳中学2022-2023学年高二下学期期末理科数学试题
陕西省渭南市合阳县合阳中学2022-2023学年高二下学期期末理科数学试题宁夏回族自治区银川一中2024届高三上学期第三次月考数学(理)试题宁夏银川市第一中学2024届高三第三次月考数学(理)试题(已下线)专题2-7 导数压轴大题归类-2(已下线)第10讲:导数期末题型突破(单调性、不等式、零点、恒成立)山东省济宁市第一中学2023-2024学年高二下学期质量检测(二)数学试题(已下线)高二下学期期末复习解答题压轴题二十二大题型专练(2)
7 . 已知抛物线
的方程为
.
(1)若M是
上的一点,点N在
的准线l上,
的焦点为F,且
,
,求
;
(2)设
为圆
外一点,过P作
的两条切线,分别与
相交于点A,B和C,D,证明:当P在定直线
上运动时,
四点的纵坐标乘积为定值的充要条件为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac62b1ade07205ae2693ec1ab135def.png)
(1)若M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb333b87ab3ecde430010b4dd8b371fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097f96fa2acd52a77bd9e2d3c33f53fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c5c639651fd0df8f041185e5c080b4.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302981b9a0645b6439fb0febfb4b1caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee2abc983789634e0e57db4576e45b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc8335f8a3b076ccd596452bad61541.png)
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2卷引用:陕西省、青海省部分学校2024届高三上学期9月联考理科数学试题
名校
8 . 已知函数
.
(1)若
在
处的切线与
平行,试分析
极值点的个数;
(2)若
有零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20e8dd2e0de7a2efdc9337c6d21885e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6982f2268e3a563e7fbd3cd58a2eaf0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc122f630d6c809acadea5380218785.png)
您最近一年使用:0次
9 . 已知函数
,
.
(1)讨论
的单调性;
(2)当
时,证明:
;
(3)证明:对任意的
且
,都有:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9787953919081e841d629fdc550ad980.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257810d08006d4b886331966c99767ea.png)
(3)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe977dbfe794d737902609918f4dec63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6470910d263157f4b7fa6809c4475c52.png)
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|
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6卷引用:陕西省咸阳市旬邑县中学2023-2024学年高三上学期开学检测理科数学试题
陕西省咸阳市旬邑县中学2023-2024学年高三上学期开学检测理科数学试题广东省广州市天河区2022-2023学年高二下学期期末数学试题(已下线)第二章 导数与函数的单调性 专题一 含参函数单调性(单调区间) 微点3 含参函数单调性(单调区间)综合训练(已下线)专题突破卷10 导数与不等式证明广东省佛山市禅城实验高级中学2023~2024学年高二下学期段考(一)数学试题(已下线)高二数学下学期期末押题试卷01
名校
10 . 如图,在四棱锥
中,
,
,
,△MAD为等边三角形,平面
平面ABCD,点N在棱MD上,直线
平面ACN.
.
(2)设二面角
的平面角为
,直线CN与平面ABCD所成的角为
,若
的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf10d92f20501e19d25f6f4159aab89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e05d8681a679bd31922e62480f69d55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451604e8cbe0706585d9cd2c76db4b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74c46a80f7540470b5e171e2e17d3bf.png)
(2)设二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698335f4880c7a298f4898c83b6562bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de9d1a07d32cae0e86d73482477da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
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2023-06-30更新
|
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8卷引用:陕西省西安市莲湖区2022-2023学年高一下学期期末数学试题