名校
1 . 已知椭圆
的右焦点是
,过点
作直线
交椭圆于点A,B,过点
与直线
垂直的射线交椭圆于点
,
,且三点
共线(其中O是坐标原点),则椭圆的离心率为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3324199c6751f2e0e6d8542783b0d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b78af48c04c69f03e32b7ef055dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b908ff79a3d103a3668b687b0e29fb.png)
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2卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
2 . 已知数列
的各项是奇数,且
是正整数
的最大奇因数,
.
(1)求
的值;
(2)求
的值;
(3)求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97daaae5be89c76c7ccb25fd96339b46.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab24d03d347b53c928e704601e68a7d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
(3)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
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3卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
3 . 已知函数
满足
0,且在
上单调递减,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3629fc26ba72d06828e15f73a0239e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa4d47243b70e8a99d92acda011d9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e67369d0580ed8c87e2f33b07b737426.png)
A.函数![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() |
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2卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
名校
解题方法
4 . 已知正实数
,记
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0fbaa3d39c022e74dd15c2984b3a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.2 | C.1 | D.![]() |
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2卷引用:辽宁省2024届高三下学期二轮复习联考(二)数学试题
名校
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
求曲线
在点
处的切线方程.
(2)若
证明:
在
上单调递增.
(3)当
时,
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb10f8ecb4ec7d3136bc662867968f2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20439836def79ea69d967d95e81320a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87676cc3ca413d9ba64fab2cd45c909c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec994bb92d9945a4369f1215d859ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5卷引用:辽宁省本溪市县级重点高中协作体2023-2024学年高二下学期期中考试数学试卷
辽宁省本溪市县级重点高中协作体2023-2024学年高二下学期期中考试数学试卷甘肃省白银市2023-2024学年高二下学期5月期中考试数学试题广东省顺德区北滘中学2023-2024学年高二下学期期中考试数学试卷内蒙古自治区兴安盟2023-2024学年高二下学期学业水平质量检测数学试题(已下线)拔高点突破03 导数中的朗博同构、双元同构、指对同构与二次同构问题(九大题型)
名校
解题方法
6 . 如图,在平面四边形
中,已知
为等边三角形,记
.
,求
的面积;
(2)若
,求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e20c68b4026751ce2f33b98a423f008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3202b1d9f838c32ab5765ce647d96b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3416881a6f67d05fe6b67787047fc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c98466484e09a9a4ff6b10785d6715.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
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3卷引用:辽宁省七校2023-2024学年高一下学期6月联考数学试卷
解题方法
7 . 已知
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046387911745f43ff3b6804ea58eb26a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6105ce0cf660bbd473c3c7008dcd8cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc903c19f7b3b0aa58cdb0cdb7b062a0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 曲线的切线、曲面的切平面在平面几何、立体几何以及解析几何中有着重要的应用,更是联系数学与物理学的重要工具,在极限理论的研究下,导数作为研究函数性质的重要工具,更是与切线有着密不可分的关系,数学家们以不同的方法研究曲线的切线、曲面的切平面,用以解决实际问题:
(1)对于函数
,分别在点
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第
项,则称数列
为函数
的“切线
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第
项,则称数列
为函数
的“切线
轴数列”.
①设函数
,记
的“切线
轴数列”为
;
②设函数
,记
的“切线
轴数列”为
,
则
,求
的通项公式.
(2)在探索高次方程的数值求解问题时,牛顿在《流数法》一书中给出了牛顿迭代法:用“作切线”的方法求方程的近似解.具体步骤如下:设
是函数
的一个零点,任意选取
作为
的初始近似值,曲线
在点
处的切线为
,设
与
轴交点的横坐标为
,并称
为
的1次近似值;曲线
在点
处的切线为
,设
与
轴交点的横坐标为
,称
为
的2次近似值.一般地,曲线
在点
处的切线为
,记
与
轴交点的横坐标为
,并称
为
的
次近似值.已知二次函数
有两个不相等的实根
,其中
.对函数
持续实施牛顿迭代法得到数列
,我们把该数列称为牛顿数列,令数列
满足
,且
,证明:
.(注:当
时,
恒成立,无需证明)
(1)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f5d05c4f3cd39f8c7350bbaa4f33f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419a7a66eae6ca3db9ec2fc97ac9e39e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596afe6f8149e39c53d36a759bee6151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be6f009bfb61b11e4f87edb4132de3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636ca879d706b6dc50b7850763170e98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4741eb4c177d75ca74fe2d36e52ecbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c120bfaa6e014c2e42b762a23e254282.png)
①设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce141de2ce7bf76952b12ad0eef31841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be6f009bfb61b11e4f87edb4132de3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
②设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8898d891410dd22bff5d1d2a3cf340e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c120bfaa6e014c2e42b762a23e254282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73f3197d32f0447314ecff34042be22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
(2)在探索高次方程的数值求解问题时,牛顿在《流数法》一书中给出了牛顿迭代法:用“作切线”的方法求方程的近似解.具体步骤如下:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228ffd36275efe54529fc0ce7c3dfadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a5b0f908cdae073db61be5b42fbcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a475fec8ded321e10a6697319fb975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b2139fd92090785e08fbdf814c41f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e34e4e8a7b5e84373ea90b0687f6e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0214c08650784be483000e2f0fc9fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ab44c68cb5ca9cc745e230f0b3aa2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d30dca4cf0e7d0774988b7312fe3378.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d992e72bcf5154fd2d26147cf0d15299.png)
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9 . (1)利用双曲线定义证明:方程
表示的曲线是焦点在直线
上的双曲线,记为曲线
;
(2)设点
在曲线
上,
在曲线
上,且满足
,求
方程;
(3)点
在
上,过点
的直线
与
的渐近线交于
,
两点,且满足
,求
(
为坐标原点)的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377a2333ff8c63cbdb20b882d6d5a7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb57bb18755127be041d346444a4743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeebe2d626de76ae34a1a42b62a1a3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eae0d794fb0823bc1545822f2f7b8db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/548e9d7ca152d84587b14b99749a339d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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解题方法
10 . 已知
是椭圆
上的动点,若动点
到定点
的距离
的最小值为1,则椭圆
的离心率的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446239fc6902eb55ad0e01d924faf592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56ab70e602f2e2e291df643ab209162.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次