名校
1 . 17世纪,法国数学家马林·梅森在欧几里得、费马等人研究的基础上,对
(
为素数)型的数作了大量的研算,他在著作《物理数学随感》中断言:在
的素数中,当
,3,5,7,13,17,19,31,67,127,257时,
是素数,其它都是合数.除了
和
两个数被后人证明不是素数外,其余都已被证实.人们为了纪念梅森在
型素数研究中所做的开创性工作,就把
型的素数称为“梅森素数”,记为
.几个年来,人类仅发现51个梅森素数,由于这种素数珍奇而迷人,因此被人们答为“数海明珠”.已知第7个梅森素数
,第8个梅森素数
,则
约等于(参考数据:
)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e9a7f85d7c3dac0c7bb7ec2dd64952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ba17b59a116513159db245f1c6d95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e9a7f85d7c3dac0c7bb7ec2dd64952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb279735edf82ac8e752afb75b7bf254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda3e08795c1ce2970f5e8743c700dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e9a7f85d7c3dac0c7bb7ec2dd64952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e9a7f85d7c3dac0c7bb7ec2dd64952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b103e029a381dc68ba5bacfd492cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa934bbf969b2093d582c75c529d6e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d847078e05bef28fbd2e85f37d6d120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87f3c9f2c83165537b05ec39e431ba02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210da5653b0cf98863ff54b341eb7019.png)
A.17.1 | B.8.4 | C.6.6 | D.3.6 |
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|
874次组卷
|
5卷引用:浙江省杭州绿城育华学校2023-2024学年高一上学期期末考试数学试题
浙江省杭州绿城育华学校2023-2024学年高一上学期期末考试数学试题福建省三明市2023届高三三模数学试题(已下线)专题4.3 对数【七大题型】-举一反三系列(已下线)4.3 对数运算(精讲)-《一隅三反》(已下线)专题21 指数、对数、幂函数小题
名校
解题方法
2 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦函数:
,双曲余弦函数:
.(e是自然对数的底数,
).
(1)计算
的值;
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
______,并加以证明;
(3)若对任意
,关于
的方程
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694af0c9f990ecb8b54b1c08bcc578e.png)
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92c32edc0e000405b7a6b9c48549959.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f78f05631a2ecb8bc3d379ca6c81f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed807cc52eca7b462a3850b5e5e02b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-06-21更新
|
1021次组卷
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8卷引用:上海市宝山区2022-2023学年高一下学期期末数学试题
上海市宝山区2022-2023学年高一下学期期末数学试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)上海市市西中学2023-2024学年高一下学期期末复习数学试卷(已下线)模块六 专题5 全真拔高模拟1(已下线)专题14 三角函数的图象与性质压轴题-【常考压轴题】山东省济南市山东师大附中2022-2023学年高一下学期数学竞赛选拔(初赛)试题(已下线)第10章 三角恒等变换单元综合能力测试卷-【帮课堂】(苏教版2019必修第二册)上海市闵行(文琦)中学2023-2024学年高一下学期3月月考数学试卷
3 . 已知
为无穷递增数列,且对于给定的正整数k,总存在i,j,使得
,其中
.令
为满足
的所有i中的最大值,
为满足
的所有j中的最小值.
(1)若无穷递增数列
的前四项是1,2,3,5,求
和
的值;
(2)若
是无穷等比数列,
,公比q是大于1的整数,
,求q的值;
(3)若
是无穷等差数列,
,公差为
,其中m为常数,且
,求证:
和
都是等差数列,并写出这两个数列的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1ded6f77356604d433281600b0a7ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/025107fcef5903df1c886118b596f037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fbaca4f2c11cb63d57e05c04b65eb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b432066a7f55ec8df55a1652f125c238.png)
(1)若无穷递增数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fdd7e9cd5d1764bc5de8add15700ae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291b233bedaa34a45e83ba88d2eb52b2.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a60e77043cfa243c212f9e340c5f46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d63107e05862f8b7ad46d2c1aa82e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/290620a953fcb6d98ef745ae64c6039a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8033f2db31435f0dc91683ff0969735a.png)
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2023-01-02更新
|
411次组卷
|
3卷引用:北京市大兴区2022-2023学年高二上学期期末数学试题
北京市大兴区2022-2023学年高二上学期期末数学试题北京市西城区北师大二附中2024届高三上学期期中数学试题(已下线)专题05 数列在高中数学其他模块的应用(九大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
名校
解题方法
4 . 集合
{
为严格增函数}.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd9d037c0d8e896aadf54a606216ed1.png)
(1)直接写出
是否属于集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb3ca04b6d34b11e4484c9537ad9a83.png)
(2)若
.解不等式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10777a53e99afc4cf30f6e1d5b0a3d12.png)
(3)
证明:“
”的充要条件是“
”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447a9718a502491b47072ce013c26a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/007dfaabad7788745505ac6363878bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd9d037c0d8e896aadf54a606216ed1.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2747dd40e29f1e55ad2c611e70a26130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb3ca04b6d34b11e4484c9537ad9a83.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac4f25a9e721472d77ad3b53e379866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10777a53e99afc4cf30f6e1d5b0a3d12.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00953787b22838f02eeaf5e485def38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56762c325380f8adf5c6021d9aaf386e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be45461ead6234f68604da537c594d3.png)
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名校
解题方法
5 . 已知两个变量
且
满足关系式
,且
是
的函数.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/18/fb160dbb-e69a-4e91-ba11-b9b90fbd9f18.png?resizew=168)
(1)写出该函数的表达式
,值域和单调区间(不必证明);
(2)在坐标系中画出该函数的图象(直接作图,不必写过程及理由).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656d649176f38261805ad14bb1066216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a0e656a2de8d47b9001cc32b1316eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b3feb5aad6b9d53cb432532681d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/18/fb160dbb-e69a-4e91-ba11-b9b90fbd9f18.png?resizew=168)
(1)写出该函数的表达式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)在坐标系中画出该函数的图象(直接作图,不必写过程及理由).
您最近一年使用:0次
解题方法
6 . 已知实数
,
,
,满足
.
(1)若
,求实数
的值;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98ea2f945ef1bfe060d334f6046091b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7eca46642891f6b8e3e30edd9b37dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/404f19c00441f801d250ae698fbfcb2f.png)
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2022-07-18更新
|
354次组卷
|
2卷引用:山东省滨州市2021-2022学年高二下学期期末数学试题
名校
7 . 已知集合
,集合
.记集合
中最小元素为
,集合
中最大元素为
.
(1)求
及
,
的值;
(2)证明:函数
在
上单调递增;并用上述结论比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f65b7a330102cc1bb508edb407d9e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74027da4c64249165c8ee966dd919273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3f58722394cad3df7234b543be4587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda591d3909af06eabf6b37c65bfe571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
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|
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4卷引用:江苏省南通市如皋中学2021-2022学年高一上学期期末数学试题
名校
解题方法
8 . 已知定义在R上的函数
满足:
在区间
上是严格增函数,且其在区间
上的图像关于直线
成轴对称.
(1)求证:当
时,
;
(2)若对任意给定的实数x,总有
,解不等式
;
(3)若
是R上的奇函数,且对任意给定的实数x,总有
,求
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ee081ef6ed3261541eade37f4f9da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ee081ef6ed3261541eade37f4f9da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ea438617b79dcfca03dacdf20929046.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
(2)若对任意给定的实数x,总有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e298fe246eef819dd9b1edabe3bb9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cbbf4d5b8ecbfccc5de39781396d07.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b762ca4a3a079282f7c2cdfc5d39f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2022-01-21更新
|
1353次组卷
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5卷引用:上海市曹杨第二中学2021-2022学年高一上学期期末数学试题
上海市曹杨第二中学2021-2022学年高一上学期期末数学试题江苏省苏州工业园区星海实验中学2022-2023学年高一上学期期中数学试题(已下线)第14讲 函数的应用与反函数(3大考点)(2)第4章 指数概念与对数函数(基础、典型、易错、新文化、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)专题16反函数-【倍速学习法】(沪教版2020必修第一册)
9 . 已知函数
.
(1)证明:
;
(2)若存在一个平行四边形的四个顶点都在函数
的图象上,则称函数
具有性质P,判断函数
是否具有性质P,并证明你的结论;
(3)设点
,函数
.设点B是曲线
上任意一点,求线段AB长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3025c3a2c23d518b088275cd348380ff.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b492f9997599d7010efc2ee1993b684a.png)
(2)若存在一个平行四边形的四个顶点都在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a525534689bd2701205d4ab17574c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b129d5bd03bd4e3895dcb15bec8eedf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
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名校
10 . 立德中学高一数学兴趣小组利用每周五开展课外探究拓展活动,在最近的一次活动中,他们定义一种新运算“
”:
,
,通过进一步探究,发现该运算有许多优美的性质:如
,
等等.
(1)对任意实数
,请判断
是否成立?若成立请证明,若不成立,请举反例说明;
(2)已知函数
,函数
,若对任意的
,存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5060d9b229d6cfc8b21ecb5549d17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64541d7f445079207b6f671adc7d662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347604752750649bde7b37c456c8263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c46a883a70c6ca89d9877ed4894bc5.png)
(1)对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee069136ee60c3983c957ba0961f912.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6051ffc0e9ae07f6dd5e8a825c02b97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/103d9319c355a06e10c118088dac5991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12965bbc260bdbb0df0a110e59fb8d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5987e76a34012a8bd0d51da0fddd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-02-02更新
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254次组卷
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2卷引用:安徽省安庆市2021-2022学年高一上学期期末数学试题