1 . 已知函数
各项均不相等的数列
满足
.令
.给出下列三个命题:(1)存在不少于3项的数列
使得
;(2)若数列
的通项公式为
,则
对
恒成立;(3)若数列
是等差数列,则
对
恒成立,其中真命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e115dd0cb0c28b33cdc1a43e9be779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6044fe76e20b5da7861f3d9b3f3143e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec26010780db181e89a51f780743f6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d87a9b5258b1a5eaee3b71004a4838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8fcccbb1234ad67314c96f9856e240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1a21f360eab1fb27b8cc15db4c04a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6273df1952961f128bb340bc28e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2cc49cadf5bf94f8df8318fa7bd519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
A.(1)(2) | B.(1)(3) | C.(2)(3) | D.(1)(2)(3) |
您最近一年使用:0次
2020-11-15更新
|
1711次组卷
|
6卷引用:2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题
2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题(已下线)数学-6月大数据精选模拟卷04(上海卷)(满分冲刺篇)上海市南洋模范中学2021届高三上学期期中数学试题(已下线)考向03 函数及其性质-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)考向15 等比数列-备战2022年高考数学一轮复习考点微专题(上海专用)上海交通大学附属中学2021-2022学年高一下学期5月线上月考数学试题
2 . 如图,椭圆
的两条弦
,
满足
,记直线
与直线
交于P点.
![](https://img.xkw.com/dksih/QBM/2020/11/7/2588053964496896/2591991184564224/STEM/51d69cc6717c4e3e927773826ef282de.png?resizew=230)
(1)求
的最大值;
(2)若P点在抛物线
上,求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b1b8a84ae7a1b2243b78cc932860d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20f230eb4f06c967f1bc104494e92cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2020/11/7/2588053964496896/2591991184564224/STEM/51d69cc6717c4e3e927773826ef282de.png?resizew=230)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224e16c7b92374d779ddeefbe9a9203d.png)
(2)若P点在抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf76958d67bce2b921af4de71572330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
20-21高二上·上海浦东新·期中
名校
3 . 在平面直角坐标系中,定义
为两点
、
的“切比雪夫距离”,又设点
及直线
上任一点
,称
的最小值为点
到直线
的“切比雪夫距离”,记作
.
(1)求证:对任意三点
、
、
,都有
;
(2)已知点
和直线
,求
;
(3)定点
,动点
满足
(
),请求出点
所在的曲线所围成图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568ac4cea4f8cf844fad9fe21a3bb2b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82923ea5d3a0b7bc6a2c529959324b0d.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/f6fb005483a774d04231b2904c05a15d.png)
(1)求证:对任意三点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad7b990a583329c302c5afb091f1ae8.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac5225ff6aa3c06ff5c8437f88093f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94922febcf02e84401ab8631890532df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fb005483a774d04231b2904c05a15d.png)
(3)定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b77e6b117cf9d90d7d31d7ebde3dbf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c459780702ffeb63d0be6deb86e7c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2020-11-12更新
|
2059次组卷
|
8卷引用:上海市华东师范大学第二附属中学2020-2021学年高二上学期期中数学试题
(已下线)上海市华东师范大学第二附属中学2020-2021学年高二上学期期中数学试题(已下线)专题19 切比雪夫(已下线)专题27 直线与圆的综合应用-1(已下线)第五篇 向量与几何 专题19 抽象距离 微点4 抽象距离综合训练(已下线)重难点突破03 直线与圆的综合应用(七大题型)北京市第八中学2020-2021学年高二下学期期末数学试题(已下线)第1章 直线与方程(章末测试基础卷)-2021-2022学年高二数学同步单元测试定心卷(苏教版2019选择性必修第一册)(已下线)难关必刷02直线与方程-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
4 . 已知集合
中的元素都是正整数,且
,集合
具有性质
:对任意的
,且
,都有
.
(1)判断集合
是否具有性质
;
(2)求证:
;
(3)求集合
中元素个数的最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f5f2024c63910786f10e6520a775fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894271881878cff367d6dee01153fde1.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36cd2052417ccb1650cc533f62273aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5a1fac2ea1080bed5e13925c6c3096.png)
(3)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
5 . 集合
且
,若
,且
,
,令
.
(1)
若
,满足
,请写出一个符合题意的
,并求出
;
(2)若集合
,任取
中2个不同的元素
,求集合
中元素个数的最大值;
(3)若存在
,使
,集合中任两个元素不同,求出此时
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afb994f4d6079603cbf46f395e512e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42276f02e595121d35171554a735f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7620daddd185dac88c3534c0dc4487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da699996ed9e57b4f536c811d64c487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9063138d7c0f40f544c275a714cc626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4d4e17981fbb90b17a8e7b47d7fa99.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0df62a2d692431f0f4c481ef7b387c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d66322be72a5324f708d09c003679f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdd3a05b298ecaec3843e99061b01cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686bd782291ddba5cd281f024c1746d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6433e0b49d284d561826900ea76a261b.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/850d5c706db7a763b0ea0117c6dc5084.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2911f1ce84be9464ba57d158ac7c6a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0606069a64e67680c15723bbc87ab59b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b98387c7606916b5cdb60266d0b5452.png)
您最近一年使用:0次
2020-11-11更新
|
944次组卷
|
2卷引用:北京市2020届高三数学高考考前冲刺模拟试题
名校
解题方法
6 . 已知函数
,
.
(Ⅰ)若
,解不等式
;
(Ⅱ)设
是函数
的四个不同的零点,问是否存在实数
,使得其三个零点成等差数列?若存在,求出所有
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e49948cb5d0925be201ed086845f1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fcc1dbd7485c0ff2a6e1ad4d871d34.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e9fa864472349a0094a4c8328e4536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/190a6120c3330c51d0823c8bd8991b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-11-08更新
|
813次组卷
|
5卷引用:浙江省丽水市2018-2019学年高一下学期期末数学试题
浙江省丽水市2018-2019学年高一下学期期末数学试题广东省执信中学2019-2020学年高二上学期9月月考数学试题(已下线)【新东方】杭州新东方高中数学试卷323(已下线)第23讲 零点问题之三个零点-突破2022年新高考数学导数压轴解答题精选精练浙江省宁波市北仑中学2022-2023学年高二(1班)下学期期中数学试题
名校
7 . 如图,已知点
,
、
为抛物线上
不同的两点(
在
的右上方,
在直线
的下方),满足
.
![](https://img.xkw.com/dksih/QBM/2020/11/3/2584971638710272/2585617836023808/STEM/d0917742-bf13-434d-8e7d-614881c7e61e.png?resizew=203)
(1)证明:
的中点
位于某定直线上;
(2)记
内切圆、外接圆的半径分别为
、
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](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/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7ce0ebe5340d3fb30e50ab560781a4.png)
![](https://img.xkw.com/dksih/QBM/2020/11/3/2584971638710272/2585617836023808/STEM/d0917742-bf13-434d-8e7d-614881c7e61e.png?resizew=203)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff3606c7bf728b4f539261461cde677.png)
您最近一年使用:0次
8 . 已知直线
:
与椭圆
:
至多有一个公共点,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bdef2df20c76169b34d896050fa6344.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2020-11-04更新
|
2766次组卷
|
4卷引用:湖北省武汉市育才中学2019-2020学年高二上学期第二次段考理科数学试题
湖北省武汉市育才中学2019-2020学年高二上学期第二次段考理科数学试题湖南省长沙市第一中学2024届高三数学新改革适应性训练一(九省联考题型)(已下线)3.2 双曲线(难点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)3.2.1 双曲线及其标准方程(重难点突破)-【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)
名校
解题方法
9 . 若
,则
的最小值是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab6ac85ab2971d2efb0eeab1704cda8f.png)
您最近一年使用:0次
10 . 已知直线
与曲线
和
分别相切于点
,
.有以下命题:(1)
(
为原点);(2)
;(3)当
时,
.则真命题的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ec45b0558fc0d3473ca9da21d5c073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bce8006396fd6519f366dc4a7cb8045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0954a8b329893eb0c5b400e3fbc4042f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b86d609bdb16f3fe441794c7140446.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a4e0d114afe36b3ad5eaac27ddee8d.png)
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A.0 | B.1 | C.2 | D.3 |
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2020-10-24更新
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1955次组卷
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5卷引用:河北省唐山市2019-2020学年高三上学期期末数学理科试题