1 . 数列
满足:
或
.对任意
,都存在
,使得
,其中
且两两不相等.
(1)若
,写出下列三个数列中所有符合题目条件的数列的序号;
①
;②
;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682443f327ff60ddf3e91cbe7821d99.png)
(2)记
.若
,证明:
;
(3)若
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32034ab9eaa06e450e27d87e999ea9e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad657749a0e222333076c72bf949970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fdb0c5b7a3e183c714fad838d246d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c639c7e5f1e7e7ee5d5ee2f30b155bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c4d0383577207858e39b4b19b0853e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454cc6ac47d35ebc2b34af6a8047a44e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5305ea58d22efe7136d404b1d44634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e44f2f5b6cab3a33e24de2502ac0c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682443f327ff60ddf3e91cbe7821d99.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6559598727fb120a5cdbf4f15510615d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743b4f6fde34464397b010cb45eabb7d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662276a5012893d881e7d1d882b5ea4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2022-05-29更新
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9卷引用:北京市西城区2018届高三期末考试理科数学试题
2 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)求函数
零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c1d48956f4aa941769df888f7aeefa.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965805ffeac6f1f1a2e3c5c7bb30676e.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8a57d5eea703c5b8980ec5c7247ff9.png)
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2020-02-09更新
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701次组卷
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2卷引用:2020届北京市通州区高三第一学期期末考试数学试题
名校
3 . 已知
均为大于0的实数,给出下列五个论断:①
,②
,③
,④
,⑤
.以其中的两个论断为条件,余下的论断中选择一个为结论,请你写出一个正确的命题___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118753a2bffc2d5de8271f3f33e812b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f4fa6828188864939832ab3c23197a.png)
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17卷引用:2020届北京市通州区高三第一学期期末考试数学试题
2020届北京市通州区高三第一学期期末考试数学试题2020届高三2月第01期(考点10)(文科)-《新题速递·数学》(已下线)专题7.1 不等式的解法-备战2021年高考数学精选考点专项突破题集(新高考地区)(已下线)考点突破02 一元二次函数-备战2022年高考数学一轮复习培优提升精炼(新高考地区专用)(已下线)专题02 不等关系-2022年(新高考)数学高频考点+重点题型浙江省温州市瑞安中学2020-2021学年高一上学期10月月考数学试题(已下线)艺体生一轮复习 第二章 集合、常用逻辑用语与不等式 第7讲 不等关系和不等式【练】(已下线)专题02 不等关系(已下线)第03章 不等式(A卷基础卷)-2020-2021学年高一数学必修第一册同步单元AB卷(新教材苏教版)(已下线)第3章 不等式(A卷-基础卷)-2021-2022学年高一数学同步单元AB卷(苏教版2019必修第一册)【学科网名师堂】(已下线)第3章《不等式》 培优测试卷(一)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)陕西省西安交通大学附属中学2022-2023学年高一上学期第一次月考数学试题(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列广东省东莞市翰林实验学校2023-2024学年高一上学期10月月考数学试题陕西省西安市雁塔区第二中学2023-2024学年高一上学期第一阶段检测数学试题(已下线)第2章 等式与不等式-【优化数学】单元测试能力卷(人教B版2019)(已下线)专题02 一元二次函数、方程和不等式3-2024年高一数学寒假作业单元合订本
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e26788a11b37ce305f080e5b24a3bc.png)
.
(1)求函数
的单调区间;
(2)求函数
的零点个数;
(3)当
时,求证不等式
解集为空集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e26788a11b37ce305f080e5b24a3bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/576e46387412fddf8bc25fda0441b090.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9959538ec4a4fe97c14d5149426fa50.png)
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2019-11-11更新
|
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3卷引用:北京市通州区2019-2020学年高三上学期期中数学试题
北京市通州区2019-2020学年高三上学期期中数学试题(已下线)专题03 拿高分题目强化卷(第三篇)-备战2021年新高考数学分层强化训练(北京专版)湖北省黄石市第一中学2019-2020学年高二下学期期末数学试题
5 . 已知点
,点
在抛物线
上,过点
的直线与直线
垂直相交于点
,
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241ce9bd28046ce9b90f43b391132884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac8d256b78ce94598538f6556cbfc6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35031ade086c0cb5adcd82aaef62462.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-09-27更新
|
2009次组卷
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6卷引用:2016届北京通州区高三4月一模数学(理)试卷
2016届北京通州区高三4月一模数学(理)试卷2017年普通高等学校招生全国统一考试(浙江卷)仿真预测卷(五)人教B版(2019) 选择性必修第一册 过关斩将 第二章 平面解析几何 2.7 抛物线及其方程 2.7.1 抛物线的标准方程(已下线)3.3 抛物线的标准方程-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册) 广西贺州市2021-2022学年高二上学期全面质量检测数学(文)试题广西贺州市2021-2022学年高二上学期全面质量检测数学(理)试题
6 . 设
为正整数,集合
.对于集合
中的任意元素
和
,记
.
(Ⅰ)当
时,若
,
,求
和
的值;
(Ⅱ)当
时,设
是
的子集,且满足:对于
中的任意元素
,当
相同时,
是偶数;当
不同时,
是奇数.求集合
中元素个数的最大值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856137172eedc26bbc4ea49915e8f6fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde12984f34f037298fa1ad2ff941b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76436f7f8f4d3396898a30f2021a6667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4c686670cb4345ae0e7282d8b1e14f.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ed7cc395c386a309ba231597a7ce71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5537c96271cd8596e00f76c96215962e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3405681d9c2b5dcf62932f3f29ad8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fb73a03dc537af4994857810edbce6.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6c3551651bc1259a97055e8b66597b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6c3551651bc1259a97055e8b66597b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abf517d1f10b5ae12a755fde12c47f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6c3551651bc1259a97055e8b66597b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79fb73a03dc537af4994857810edbce6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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7 . 一个大于1的自然数,除了1和它本身外,不能被其他自然数整除,则称这个数为质数.质数的个数是无穷的.设由所有质数组成的无穷递增数列
的前
项和为
,等差数列1,3,5,7,…中所有不大于
的项的和为
.
(Ⅰ)求
和
;
(Ⅱ)判断
和
的大小,不用证明;
(Ⅲ)设
,求证:
,
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960b682f983b053dc9064cf29c97e250.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/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e727bd61ff43fe654f6532abe939b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3627e4ccde7d69c49034a4a2d10bee5.png)
(Ⅱ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
(Ⅲ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05becbd3c66ebe95299916c1c2279392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5141a5b907f5ff11bbd7cacbd7b5db3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c8a8e9b48cd1a519793b3fd840a522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7024231adcecb545198697a2037efe.png)
您最近一年使用:0次
名校
8 . 已知函数
.
Ⅰ
若函数
的最大值为3,求实数
的值;
Ⅱ
若当
时,
恒成立,求实数
的取值范围;
Ⅲ
若
,
是函数
的两个零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae9a1e0b6c6bd250c09cd197486d3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5b76ee3bcd1abe78a0d22df47b4773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1de4aed718a98bd09c56f96de92851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040135d64192de075ba0cc9f11ddbc9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa33c2bd791339d32821077846605d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d6fe150b0a721696c8c063999ba38d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c89eea81aaf07c12b494125ed4e056.png)
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|
738次组卷
|
3卷引用:【区级联考】北京市通州区2019届高三上学期期中考试数学(理)试题
名校
9 . 已知函数
,设
在
上的最大值为
,
Ⅰ
求
的表达式;
Ⅱ
是否存在实数
,使得
的定义域为
,值域为
?如果存在,求出
的值;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ccd0c948b71d2756e7fc8effed03a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e59103d4860ccfce81d2182d66bb8d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df08979e3fac3d08f849964e68312f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df08979e3fac3d08f849964e68312f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5df08979e3fac3d08f849964e68312f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184390adf1777b9bbfbd55b8a988468a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee9ff4b397df8a64bf99d784026059b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
您最近一年使用:0次
2018-12-12更新
|
743次组卷
|
3卷引用:【区级联考】北京市通州区2019届高三上学期期中考试数学(理)试题
【区级联考】北京市通州区2019届高三上学期期中考试数学(理)试题2020届北京市海淀区首都师范大学附属中学高三开学考试数学试题(已下线)3.2.1.2 函数的最大值、最小值(课时作业)-2020-2021学年上学期高一数学同步精品课堂(新教材人教版必修第一册)
10 . 已知函数
的定义域是
,且有极值点.
(1)求实数
的取值范围;
(2)求证:方程
恰有一个实根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2106b8bb6d3ac149a046cc0aae460ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb381ac86308c6249bc7e8737cdc668d.png)
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