1 . 已知函数
.
(1)若
在定义域内单调递增,求
的取值范围;
(2)若函数
有两个极值点
,且
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b60273496e0ad78a7b32da0f05e64d1d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ec63161022b3842f19bcd12d44d45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2 . 已知点
,
,
,
均在半径为
的球面上,
是等边三角形,
平面
,则四面体
体积的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334a5773c8d24f29ec3231075170e4f8.png)
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3 . 已知若函数
有两个零点,则
的取值范围为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知函数
.
(1)若函数
的图象与直线
相切,求实数
的值;
(2)若函数
有且只有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fe84ecdcafb66c2e3a4dd702503729.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e96727a1bc483af6f4861ce6f16c66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-09-01更新
|
861次组卷
|
3卷引用:河南省开封市通许县2023届高三冲刺(四)文科数学试题
解题方法
5 . 已知函数
,若关于
的方程
在
上有解,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732e0982b021f9857b20e4118a636bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0435ec89a0138f0b803d3b44db0bce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c918ca5d4e6d46ed130f85e5fa608d.png)
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6 . 已知函数
.
(1)讨论
的单调性;
(2)若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5f016b5e71cb07755393523e0bce02.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/042aef24911017ca202c1d7cf62dc005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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7 . 某校数学组老师为了解学生数学学科核心素养整体发展水平,组织本校8000名学生进行针对性检测(检测分为初试和复试),并随机抽取了100名学生的初试成绩,绘制了频率分布直方图,如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/29/bb56fa6c-a68d-4a50-bc5b-a48f596f6b44.png?resizew=235)
(1)根据频率分布直方图,求样本平均数的估计值;
(2)若所有学生的初试成绩
近似服从正态分布
,其中
为样本平均数的估计值,
.初试成绩不低于90分的学生才能参加复试,试估计能参加复试的人数;
(3)复试共三道题,规定:全部答对获得一等奖;答对两道题获得二等奖;答对一道题获得三等奖;全部答错不获奖.已知某学生进入了复试,他在复试中前两道题答对的概率均为
,第三道题答对的概率为
.若他获得一等奖的概率为
,设他获得二等奖的概率为
,求
的最小值.
附:若随机变量
服从正态分布
,则
,
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/29/bb56fa6c-a68d-4a50-bc5b-a48f596f6b44.png?resizew=235)
(1)根据频率分布直方图,求样本平均数的估计值;
(2)若所有学生的初试成绩
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfc26b8bdcd1fd3781c4593217c725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e525d9683f8c8aea32d70301662c87.png)
(3)复试共三道题,规定:全部答对获得一等奖;答对两道题获得二等奖;答对一道题获得三等奖;全部答错不获奖.已知某学生进入了复试,他在复试中前两道题答对的概率均为
![](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/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
附:若随机变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfc26b8bdcd1fd3781c4593217c725e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0af927536479e1c4a6eaa423c9ce025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06fd2142e90345e9f81cdc9c7d6d2a9.png)
您最近一年使用:0次
2023-04-28更新
|
1607次组卷
|
7卷引用:河南开封市五县2022-2023学年高二下学期第二次月考联考数学试题
解题方法
8 . 若数列
满足
,(
,
,P为常数),则称
为“等方差数列”.记
为正项数列
的前n项和,已知
为“等方差数列”,且
,
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44818d415cf4e4af51151193e204bdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9644285e2f072dfee040deaee33b4af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caac738be34e0499c837f48c06b76b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2f92296e96b4552e38adee06620ce02.png)
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9 . 对于函数
,若存在
,则称点
与点
是函数的一对“隐对称点”.若
时,函数
的图象上只有1对“隐对称点”,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12276d12c3a526fba7efbeee2c62ca39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0822798eb0f83d8dbe267aaf0d388da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bdfd867a8a7b9138d7c3c4b7e956989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
您最近一年使用:0次
2023-04-17更新
|
335次组卷
|
4卷引用:河南省开封市五县2022-2023学年高二下学期期中考试数学试卷
解题方法
10 . 已知函数
图象上三个不同的点
.
(1)求函数
在点P处的切线方程;
(2)记(1)中的切线为l,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f3c6d8a4a4ccb838e6220f4b07cc07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0e6756f722a6e745c2ff81f71bb04.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记(1)中的切线为l,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f6079d1b0033b46fe2909ea602d1e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6000852209ab28bf6ee3c3af583052.png)
您最近一年使用:0次