2024·全国·模拟预测
名校
解题方法
1 . 已知椭圆
的离心率为
,且过点
.若斜率为
的直线
与椭圆
相切于点
,过直线
上异于点
的一点
,作斜率为
的直线
与椭圆
交于
两点,定义
为点
处的切割比,记为
.
(1)求
的方程;
(2)证明:
与点
的坐标无关;
(3)若
,且
(
为坐标原点),则当
时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cda9ce6d633bc1f3a249fb0fc458a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17bcf83ec075e94f9c6a543afcad7a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44884f3ac15e7dd933e044aad80d678.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44884f3ac15e7dd933e044aad80d678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dea40504f399f4e364f2f7219bf61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e0d700800ec8282168f975dcb7f273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce662cd099fa16b8b4f900cd1f90177e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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4卷引用:吉林省通化市梅河口市第五中学2024届高三三模数学试题
吉林省通化市梅河口市第五中学2024届高三三模数学试题(已下线)高三数学考前押题卷2(已下线)安徽省合肥市第一中学2024届高三下学期三模数学试题2024届普通高招全国统一考试临考预测押题密卷数学试题(A卷)
2 . 对于任意给定的四个实数
,
,
,
,我们定义方阵
,方阵
对应的行列式记为
,且
,方阵
与任意方阵
的乘法运算定义如下:
,其中方阵
,且
.设
,
,
.
(1)证明:
.
(2)若方阵
,
满足
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e84c30444f13d37ada78285dc4f83b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e76d1d8e50dda4d50229a8a20c57e58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc29ee719feeedfbc8c529cf11348abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e11a5b70e1e2e685d1783a4707872e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ec97af19b15cd584710a3faf30c716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f44b167b4e75af29a18637f71f3ebfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39fcc210ec89dbc7d684a70a34542c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d17ebf9f595cdb9dab841dec703b512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a4ed514630bd37fab9765b3fb5f2cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/709d09c76c222f156df31a1bba5f2ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e4a35eca00ea2f4580d62515d54d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95035eeae686e910be45f08093e406c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e7d309cb178b71c6e56f5b7f610413.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109b4ece615b08a89a7f69d436f448b0.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb109c49695bce8c5b5cf4fad95772.png)
(2)若方阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2221c60bc15c59fa1b3ac74a23b57cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fa9bfe3bf3e3b7265da3c49d31f1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35536fb98d8b24cead230c8df95fd9d3.png)
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2024-06-13更新
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3卷引用:吉林省通化市梅河口市第五中学2024届高考模拟预测数学试题
3 . 已知数列
的前
项和为
,若数列
满足:①数列
项数有限为
;②
;③
,则称数列
为“
阶可控摇摆数列”.
(1)若等比数列
为“10阶可控摇摆数列”,求
的通项公式;
(2)若等差数列
为“
阶可控摇摆数列”,且
,求数列
的通项公式;
(3)已知数列
为“
阶可控摇摆数列”,且存在
,使得
,探究:数列
能否为“
阶可控摇摆数列”,若能,请给出证明过程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4ed75729a7f7a2d5a3d9f7293c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1798fb0c31c65218cd20e07320a17d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdaa641d2e7e17904c61ff7245a5cb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)若等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7364bbda64feeb4d448f9316d4c67a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad491e5b5e14c49ef8b7004ebcfcef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa22ba45c62adc96ffe508594edd6900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca8076f0553088afded57b48009d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae2ea9de54e074c145b8259f6c55e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2024-03-21更新
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1440次组卷
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6卷引用:吉林省通化市梅河口市第五中学2024届高三下学期二模数学试题
吉林省通化市梅河口市第五中学2024届高三下学期二模数学试题吉林省白山市2024届高三第二次模拟考试数学试题江西省2024届高三下学期二轮复习阶段性检测数学试题山东省淄博市实验中学2023-2024学年高二下学期第一次月考(3月)数学试卷(已下线)数学(广东专用01,新题型结构)(已下线)压轴题05数列压轴题15题型汇总-1
名校
解题方法
4 . 已知
为椭圆
上一点,点
与椭圆
的两个焦点构成的三角形面积为
.
(1)求椭圆
的标准方程;
(2)不经过点
的直线
与椭圆
相交于
两点,若直线
与
的斜率之和为
,证明:直线
必过定点,并求出这个定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)不经过点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-19更新
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13卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二下学期开学考试数学试题
吉林省通化市梅河口市第五中学2023-2024学年高二下学期开学考试数学试题四川省雅安市天立高级中学2022-2023学年高二上学期第三次月考数学(文)试题四川省雅安市天立高级中学2022-2023学年高二上学期第三次月考数学(理)试题福建省永春华侨中学2023-2024学年高二上学期期中考试数学试题山西省太原市山西大学附属中学校2023-2024学年高二上学期期中考试数学试题福建省莆田市第三中学2024届高三上学期期中数学试题(已下线)高二数学上学期期中模拟卷01(原卷版)广东省深圳市龙岗区华中师范大学龙岗附属中学2023-2024学年高二上学期期末区统考模拟考试数学试卷四川省泸州市合江县马街中学校2023-2024学年高二上学期期末数学试题(已下线)专题03 圆锥曲线的方程(3)(已下线)微考点6-3 圆锥曲线中的定点定值问题(三大题型)(已下线)专题10 椭圆的几何性质8种常见考法归类(2)(已下线)专题08 圆锥曲线 第二讲 圆锥曲线中的定点、定直线与定值问题(分层练)
名校
5 . 黎曼猜想是解析数论里的一个重要猜想,它被很多数学家视为是最重要的数学猜想之一.它与函数
(
,s为常数)密切相关,请解决下列问题.
(1)当
时,讨论
的单调性;
(2)当
时;
①证明
有唯一极值点;
②记
的唯一极值点为
,讨论
的单调性,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755d78f27a96bf14b96dff9913851df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b862659eee15ac003d2d2c53d9abbf5c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b366d99460274e9ab2187c11af8a6372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f15bcd4917a74ec6f505f0e10833a7f.png)
①证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010dec4fc2df0b58992eb4515cd13eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010dec4fc2df0b58992eb4515cd13eff.png)
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2024-01-15更新
|
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9卷引用:吉林省通化市梅河口市第五中学2024届高三下学期一模数学试题
吉林省通化市梅河口市第五中学2024届高三下学期一模数学试题2024届广东省惠州市大亚湾区普通高中毕业年级联合模拟考试(一)数学试卷2024届广东省大湾区普通高中毕业年级联合模拟考试(一)数学试题湖南省长沙市长郡中学2024届高三一模数学试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编天津市第一中学滨海学校2024届高三第六次学业水平质量调查数学试卷(开学考)(已下线)专题2 导数与函数的极值、最值【练】辽宁省锦州市某校2023-2024学年高三下学期考前测试数学试卷(A)河南省信阳市新县高级中学2024届高三考前第七次适应性考试数学试题
名校
解题方法
6 . 英国数学家泰勒发现了如下公式:
其中
为自然对数的底数,
.以上公式称为泰勒公式.设
,根据以上信息,并结合高中所学的数学知识,解决如下问题.
(1)证明:
;
(2)设
,证明:
;
(3)设
,若
是
的极小值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6696028290bbaddf628d64bad0ed95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2976d45a26ec77149a05553e8eb13efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78478b44ff22e088fd8e6522c5d78a2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d84ae7f43ef85da907d2917ff5f2a80.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8586154d8c4fb5fef893d39a7701f921.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde823e2e88ecb6045d66d61962259b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-03更新
|
2367次组卷
|
19卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题
吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题贵州省贵阳市2024届高三下学期适应性考试数学试卷(一)贵州省安顺市2024届高三下学期模拟考试(一)数学试卷云南省玉溪市第一中学2023-2024学年高二下学期3月月考数学试题海南省海南华侨中学2023-2024学年高三下学期第二次模拟考试数学试题重庆市礼嘉中学2023-2024学年高二下学期第一次月考数学试题重庆第十一中学校2023-2024学年高二下学期3月月考数学试题重庆市璧山中学校2023-2024学年高二下学期第一次月考数学试题广东省东莞市光明中学2023-2024学年高二下学期第一次月考数学试题四川省达州外国语学校2023-2024学年高二下学期3月月考数学试题黑龙江省哈尔滨市双城区兆麟中学2023-2024学年高二下学期第一次月考(4月)数学试题重庆市荣昌中学校2023-2024学年高二下学期4月期中考试数学试题广东省广州市广州中学2023-2024学年高二下学期期中考试数学试题江西省宜春市上高二中2024届高三下学期5月月考数学试卷(已下线)专题11 利用泰勒展开式证明不等式【练】河北省石家庄四十一中2023-2024学年高二下学期第一次月考数学试题河北省石家庄二中润德中学2023-2024学年高二下学期第一次月考数学试题福建省宁德市古田县第一中学2024届高中毕业班高考前适应性测试数学试题四川省南充市白塔中学2023-2024学年高二下学期期中考试数学试题
名校
7 . 已知函数
.
(1)讨论
的单调性;
(2)设
,若
,
是
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b450287f8fa1f4687f3efc3fd7444e2e.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4fa78856909db6d9e7c43078bcc7ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c4588a79e160bca3711b1151a52f26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd330acca8e17f5ff9aca1f0f312df50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1b9f152654fd42b112adb81a5879bc.png)
您最近一年使用:0次
2023-11-09更新
|
617次组卷
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5卷引用:吉林省梅河口市第五中学2023-2024学年高三上学期期中数学试题
名校
解题方法
8 . 已知双曲线
的左、右焦点分别为
,
.
(1)若点
,
在双曲线C上,求C的方程;
(2)若点P为双曲线C右支上一点,I为
的内心,且
,过原点O作PI的平行线交
于点K,求证:
,且点I的横坐标等于PK的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0813ffee858d72c088375b58797d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac596b90c2d071e5fd655e15055ad62.png)
(2)若点P为双曲线C右支上一点,I为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f21c64e8c59bcc7dfcb3339968fd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b6ccaa6f14b331b6c93461dfd933f3.png)
您最近一年使用:0次
名校
解题方法
9 . 已知双曲线C:
的左、右焦点分别为
,
,且
,若C上的点M满足
恒成立.
(1)求C的方程;
(2)若过点M的直线l与C的两条渐近线交于P,Q两点,且
.
(i)证明:l与C有且仅有一个交点;
(ii)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4f7e7f33963df24d6a46067b4677e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cdb28eafa72ace7027ac32d7dae0906.png)
(1)求C的方程;
(2)若过点M的直线l与C的两条渐近线交于P,Q两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac480bb785925885de84d8284c428830.png)
(i)证明:l与C有且仅有一个交点;
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b206caf5ac005c8df99c13b258d3e179.png)
您最近一年使用:0次
2023-08-05更新
|
564次组卷
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4卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题
名校
10 . 已知函数
,其中
.
(1)若
,讨论函数
的单调性;
(2)已知
,
是函数
的两个零点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86187410f634d2f68704b05d9ee49d99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6a8b94c02716736000e2e817b532a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7825b129635e3c3c4aba6f17aa0007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684bcf84f0a266515bfafde0da903050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3c7bb85e44e9fdeb0a51875fb8804b.png)
您最近一年使用:0次
2023-07-18更新
|
510次组卷
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4卷引用:吉林省通化市梅河口市第五中学2022-2023学年高二下学期期末数学试题