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1 . 水平相当的甲、乙、丙三人进行乒乓球擂台赛,每轮比赛都采用3局2胜制(即先贏2局者胜),首轮由甲乙两人开始,丙轮空;第二轮由首轮的胜者与丙之间进行,首轮的负者轮空,依照这样的规则无限地继续下去.
(1)求甲在第三轮获胜的条件下,第二轮也获胜的概率;
(2)求第
轮比赛甲轮空的概率;
(3)按照以上规则,求前六轮比赛中甲获胜局数的期望.
(1)求甲在第三轮获胜的条件下,第二轮也获胜的概率;
(2)求第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)按照以上规则,求前六轮比赛中甲获胜局数的期望.
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昨日更新
|
515次组卷
|
3卷引用:辽宁省大连市部分学校2024届高三下学期联合模拟考试数学试题
辽宁省大连市部分学校2024届高三下学期联合模拟考试数学试题浙江省北斗星盟2023-2024学年高二下学期5月阶段性联考数学试题(已下线)专题06 离散型随机变量与正态分布--高二期末考点大串讲(苏教版2019选择性必修第二册)
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2 . 平均值不等式是最基本的重要不等式之一,在不等式理论研究和证明中占有重要的位置,基本不等式
就是最简单的平均值不等式.一般地,假设
为n个非负实数,它们的算术平均值记为
(注:
),几何平均值记为
亦(注:
),算术平均值与几何平均值之间有如下的关系:
,即
,当且仅当
时等号成立,上述不等式称为平均值不等式,或简称为均值不等式.
(1)已知
,求
的最小值;
(2)已知正项数列
,前n项和为
.
(i)当
时,求证:
;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb90c316d8a99694396de80ed0b0cf25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62039675c3c14eb40435c837baac504b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/616f78142aa5d339a92737356cb5f034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3381745623cb1a441da9c0d591eb5fa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7cdd81b8b615961adae7ec165aacfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/434d0c6ca47b1b7af2f3ff0b7663d908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c294bd0c22262b46c1ba57f8f1dc8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cc4e11e7cd0174262dfe66662a6a33.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d229cbec798c9c278a9b5979cb38247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59149e37a56078d30e6e734fde3d6f5f.png)
(2)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d72bba8881efc02361163a97c6dde32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9021d923afeecdbb8c55e283c26704a.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237e3090bb2c02d7b62fa5d3d41b63b5.png)
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3 . 已知数列
满足
,
,令
.
(1)求证:数列
为等差数列;
(2)设
,数列
的前n项和为
,定义
为不超过x的最大整数,例如
,
,求数列
的前n项和
.(参考公式:
)
![](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/e89bddd9c021a9caccc72cd0189e1ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f0c1d9900e8c040d86a68deecb4a73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc995d4dc915fce7b9aa2a580a250d1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b3bdab0058f097f736bbcb844442f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c04c237a58b94d06952c208e18a5cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a2b1ba86f57af9387eff5d8298cbef.png)
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解题方法
4 . 某类型的多项选择题设置了4个选项,一道题中的正确答案或是其中2个选项或是其中3个选项.该类型题目评分标准如下:每题满分6分,若未作答或选出错误选项,则该题得0分;若正确答案是2个选项,则每选对1个正确选项得3分;若正确答案是3个选项,则每选对1个正确选项得2分.甲、乙、丙三位同学各自作答一道此类题目,设该题正确答案是2个选项的概率为
.
(1)已知甲同学随机(等可能)选择了2个选项作答,若
,求他既选出正确选项也选出了错误选项的概率;
(2)已知乙同学随机(等可能)选出1个选项作答,丙同学随机(等可能)选出2个选项作答,若
,试比较乙、丙两同学得分的数学期望的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(1)已知甲同学随机(等可能)选择了2个选项作答,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
(2)已知乙同学随机(等可能)选出1个选项作答,丙同学随机(等可能)选出2个选项作答,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a18d2bd429301b5478dcd26c572266.png)
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2024-05-14更新
|
980次组卷
|
3卷引用:辽宁省沈阳市翔宇中学2023-2024学年高二下学期6月月考数学试题
5 . 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)
您最近一年使用:0次
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6 . 2024年两会报告中提出“大力推进现代化产业体系建设,加快发展新质生产力”,所谓新质生产力,是创新起主导作用、以科技创新作为核心要素的先进生产力质态.今年全国两会,“新质生产力”已经成为C位热词.某创新公司落实两会精神,准备年初用980万元购买新设备用来创新,第一年使用的各种创新费用120万元,以后每年还要持续增加创新费用40万元,公司每年经过创新后的收益为500万元.
(1)问创新公司第几年开始获利?
(2)经过多少年创新公司获得的年平均利润最大?最大年平均利润是多少?
(1)问创新公司第几年开始获利?
(2)经过多少年创新公司获得的年平均利润最大?最大年平均利润是多少?
您最近一年使用:0次
名校
解题方法
7 . 定义:若函数
的值域是定义域的子集,则称
是紧缩函数.
(1)试问函数
是否为紧缩函数?说明你的理由.
(2)若函数
是紧缩函数,求
的取值范围.
(3)已知常数
,函数
,
是紧缩函数,求
的取值集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)试问函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef555a47258a9ce115189413c2e4ee63.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50ca1eddc194c3069d1caa62ff3a3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed228ab22e5d51eea0c12215e1dafe8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21cef43169928473f9145e7df54edef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-04-15更新
|
259次组卷
|
3卷引用:辽宁省辽阳市集美中学2023-2024学年高一下学期4月月考数学试题
名校
8 . 三角函数的定义是:在单位圆C:
中,作一过圆心的射线与单位圆交于点P,自x轴正半轴开始逆时针旋转到达该射线时转过的角大小为θ,则P点坐标为
,转动中扫过的圆心角为θ的扇形,由圆弧面积公式和弧度角的定义,可知面积
.类似地对于双曲三角函数有这样的定义:在单位双曲线E:
中,过原点作一射线交右支于点P,该射线和x轴及双曲线围成的曲边三角形面积是
,双曲角
,则P的坐标是
.其中,
称为双曲余弦函数,
称为双曲正弦函数同样,有类似定义双曲正切函数
双曲余切函数
且有如下关系式:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d279cc5e9f902480c9a0ea810cf9d3a.png)
,
的初等函数表达式.
(Ⅰ)双曲三角函数有如下和差公式,请任选其一进行证明:
①
;
②
;
(Ⅱ)①求函数
在R上的值域;
②若对
,关于x的方程
有解,求实数a的取值范围.
类似三角函数的反函数,试研究双曲三角函数的反函数artanhx,arcothx.
(2)①证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b450e870513b9cf6021b6416959224.png)
②已知
的级数展开式为
,写出
的级数展开式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b93ac1e1087ef8a7827e22983ab895f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33074bee68ff41ba4c6b675578f19957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050c00da6d39ad0fae411836b0a26979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15cd370bd2337b78fe820b7b61438c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2dc9ac6460d3c72e915e93b9f16d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1fe4e3a61667cfe81973a300859f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a252d4a56c74a8829afb1fccbe09d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0961cbc097652b999cd4106c671e4cd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d279cc5e9f902480c9a0ea810cf9d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53b8e0108664bf39aa302570457199a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7c627427318b62d977ff7a86c2cb5.png)
(Ⅰ)双曲三角函数有如下和差公式,请任选其一进行证明:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1079114cdde9367a22632b0165f1a1a8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3510bba38a7f232cc4d9e437e78f5b6a.png)
(Ⅱ)①求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e154c56d574646a2a541a3fe70c6307b.png)
②若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f2372e3d0c3de8f5f0579312efe38b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937c47cddd4b31aeacfad8f81705b827.png)
类似三角函数的反函数,试研究双曲三角函数的反函数artanhx,arcothx.
(2)①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b450e870513b9cf6021b6416959224.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802ae3e64c0bb802cc83bf3cf81bfe49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1bbb717893d3adb6ce58b3a99bc257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc0593e23740ebd0cd068a2eadf059e3.png)
您最近一年使用:0次
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解题方法
9 . 已知函数
,将函数
的图象上的点纵坐标不变,横坐标变为原来的
倍,再向右平移
个单位长度,得到函数
的图象.
(1)写出函数
的解析式;
(2)试判断
,
,
的大小;
(3)如果函数
的定义域为
,若对于任意
,
,
,
分别为某个三角形的边长,则称
为“三角形函数”.记
,当定义域为
时,
为“三角形函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368c73c5b1fc66954165a11ebd9bba5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ce6538c92bc0e9d9472b8077f51e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7200b19ef5b480d90ceacc189fe181b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d2e52a48a1354e7332e62aa1400104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87ff3d50d490895bfdd15748cbc56e7c.png)
(3)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c745613b6793bc25c3294ea4fdf7a288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0147d2411613220845231f6fe0cac0bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f0f5e409eba7972181c22b1e130316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a51dda51f07086ef1e52ccd5fc5e32a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c388166862b3ccfcc7ca749ebe5949.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317285a1c0d9ca521bc08812a82857f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0b1b34a0cb69bd9e0a4622b6352968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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10 . 辽宁省朝阳市妇联发挥阵地优势,在市妇女儿童活动中心开展了“萌童成长”寒假公益课堂,涵盖了创意美术、传统文化、科学小实验、“亲子阅读”等丰富的活动. 公益课堂共开设24期,近200名少年儿童受益. 从参加公益课堂的少年儿童中随机抽取50名少年儿童进行问卷调查(满分100分),将问卷调查结果按
,
,
,
,
,
,
,
分成八组,并绘制成频率分布直方图,如图所示.
的值,并估计被抽取的50名少年儿童问卷调查结果的平均数(同一组数据用该组区间的中点值作代表);
(2)若从样本中问卷调查结果在
和
内的少年儿童中随机抽取2名少年儿童,求随机抽取的这2名少年儿童在同一组的概率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621a55980e5ec656ffb86754d9aed2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509ac7d8f9fb49f871c656fde6623569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2a4c22dec305ed8c324edd85f92e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e561e9d5ec54aa011a48f21091060df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef73adfa739baccec83ad900bc48ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8a08a91c7ef462bd412bc3074bd621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e302fb0232370efe01b304fba3e4e2e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b847f8b78aa55371aecd21d8cdfed10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若从样本中问卷调查结果在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f8a08a91c7ef462bd412bc3074bd621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b847f8b78aa55371aecd21d8cdfed10.png)
您最近一年使用:0次
2024-04-11更新
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443次组卷
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5卷引用:辽宁省辽阳市集美中学2023-2024学年高一下学期4月月考数学试题
辽宁省辽阳市集美中学2023-2024学年高一下学期4月月考数学试题辽宁省部分高中2023-2024学年高一下学期4月联考数学试题(已下线)15.2 随机事件的概率-【帮课堂】(苏教版2019必修第二册)(已下线)专题10.1 随机事件与概率-举一反三系列(人教A版2019必修第二册)(已下线)10.1.3 古典概型-同步精品课堂(人教A版2019必修第二册)