1 . (1)已知
求函数
最小值,并求出最小值时
的值;
(2)问题:正数
满足
,求
的最小值.其中一种解法是:
,当且仅当
且
时,即
且
时取等号.学习上述解法并解决下列问题:若实数
满足
,试比较
和
的大小,并指明等号成立的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27d34123f3dcdf9db269c0d1e9d7802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893acd5e191b6fee8e6cc70afb4a0091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)问题:正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57f879f6e8df7d5fb261328806260b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca07c22ee28e662b8cea8d96f3f7027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c34bb88b7df81b0a9cc4f5f532f529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f86c800af77b70d7799500a45f91721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddab9f2cdfbb37f5d5845e7943910624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2edfccf9159bb4010669e938f788149b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09ffc1644c7029219b88232145abbdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47e32a3a39e310fe224a979e0cafce49.png)
您最近一年使用:0次
解题方法
2 . “绿色出行,低碳环保”已成为新的时尚.近几年,国家相继出台了一系列的环保政策,在汽车行业提出了重点扶持新能源汽车的政策,为新能源汽车行业的发展开辟了广阔的前景.某公司对
充电桩进行生产投资,所获得的利润有如下统计数据.
(1)已知可用线性回归模型拟合y与x的关系,求其线性回归方程.
(2)判断
与
的大小,并说明理由.
参考数据:
,
.
参考公式:线性回归方程中
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![]() ![]() | 3 | 4 | 6 | 7 | 9 | 10 |
所获利润![]() | 1.5 | 2 | 3 | 4.5 | 6 | 7 |
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ad777ae637a95ca6165aa1e4f45bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9028c2427614625d037c90c226899d40.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ae1aa186de468239aa3d1db1e31038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8bcdf79990ab8e0e705fbf3f31abe.png)
参考公式:线性回归方程中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183200de4ff08be4eb636e8169c099a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58291bd91befe1061530246da983727.png)
您最近一年使用:0次
3 . 若实数
满足
,则称
比
远离
.
(1)若
比
远离1,且
,求实数
的取值范围;
(2)对任意两个不相等的实数
,证明
比
远离
;
(3)若
,试问:
与
哪一个更远离
?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d32d4403d0e81eacfbe429dc51f07f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b782dd2de9c9caa840838cd63d817de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)对任意两个不相等的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b0bcc077bc78b7aae05b0c9dff42b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb3f034eb004e6db6c58a3bcd7d18cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ebc856291255f2d4a6c20b982a2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
您最近一年使用:0次
2023-08-08更新
|
244次组卷
|
2卷引用:江苏省盐城市阜宁县2022-2023学年高一上学期期中数学试题
4 . 已知
,
.
(1)求
的值;
(2)若
,请比较
与
的大小关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5bf1fbb7d7339058beb960a4c6ae5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9fb3a743c6446a007aacb91a7e0e9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beb179e422f7d680b9edba52d9478a3b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9497f07a6499d590b4d22769f353548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e53857dcc68047c16daf7a5472feda3.png)
您最近一年使用:0次
名校
5 . 已知对于正数
、
,存在一些特殊的形式,如:
、
、
等.判断上述三者的大小关系,并证明.
![](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/d24d5c95a310a34c2bcfa644c1bb5b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc8b26fb79c1f4d36130c41b18c0f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f89a8b5cf6996a6455375e405bfb9d.png)
您最近一年使用:0次
2021-11-17更新
|
146次组卷
|
4卷引用:河南省实验中学2021-2022学年高二上学期期中数学(文)试题
河南省实验中学2021-2022学年高二上学期期中数学(文)试题河南省中原名校2021-2022学年高二上学期12月联考文科数学试题河南省顶尖名校2021-2022学年高二上学期第二次素养调研文科数学试题(已下线)高一上学期第一次月考十四大题型归纳(基础篇)-举一反三系列
解题方法
6 . 已知函数
在
上单调递减.
(1)求实数
的取值范围;
(2)当实数
取最大值时,方程
恰有二解,求实数
的取值范围;
(3)若
,求证:
.(注:
为自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b8744c94d54246ce023e8a88b998c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d303edb2b74f0152e9da9e0b77a1ca37.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f826c4322fdbf0838670d917f7735e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f86f9b0f357d6166ebc79012bf88706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55278cd8cbc74b25a26141e20fe78e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9003a22f3bfbdc2dba7869c0f7d54c8c.png)
您最近一年使用:0次
名校
解题方法
7 . (1)
,比较
与
的大小;
(2)已知
,求代数式
的最小值及取最小值时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62cb1e76892ab98db3d613cd4dca609c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67336ccd79b321083fa8821e524c7467.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3fcfd03d0984df57c148db12a04049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
您最近一年使用:0次
2021-09-01更新
|
1759次组卷
|
4卷引用:上海市闵行区古美高级中学2020-2021学年高一上学期期中数学试题
上海市闵行区古美高级中学2020-2021学年高一上学期期中数学试题(已下线)专题07 基本不等式压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)湖南省长沙市第一中学2022-2023学年高一上学期第一次阶段性检测数学试题(已下线)2.2 基本不等式(第1课时)(分层练习)-【上好课】
名校
解题方法
8 . 如图所示为一个半圆柱,
为半圆弧
上一点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/a4bf1bc1-bee0-46d6-83c9-71497aa77f09.png?resizew=124)
(1)若
,求四棱锥
的体积的最大值;
(2)有三个条件:①
;②直线
与
所成角的正弦值为
;③
.请你从中选择两个作为条件,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2395720e6d6aeb7efdcd8e921849acf4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/a4bf1bc1-bee0-46d6-83c9-71497aa77f09.png?resizew=124)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a65b94de267eb6858634181642c65c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
(2)有三个条件:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b0f78a8003789a66fa4cb38a84858c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411f35f7181f79573bbfab44ea77ff1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62871bb0dff211fc3bd80f9066c25b29.png)
您最近一年使用:0次
2021-01-02更新
|
1642次组卷
|
5卷引用:T8联考八校2020-2021学年高三上学期第一次联考数学试题
T8联考八校2020-2021学年高三上学期第一次联考数学试题江苏省南京市秦淮中学2021届高三下学期期初学情调研数学试题(已下线)专练11 空间向量与立体几何综合检测(A卷)-2021-2022学年高二数学上册同步课后专练(人版A版选择性必修第一册)2023版 湘教版(2019) 选修第二册 过关斩将 第2章 空间向量与立体几何山东省济宁市育才中学2022-2023学年高二上学期第一次学情检测数学试题
名校
解题方法
9 . 设函数
,当
时,
,且对任意实数
、
满足
,当
时,
.
(1)求证:函数
在
上为单调递增函数;
(2)当
时,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a5473402bf857ed42f4084e7e6f0cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7708640b13e4a01faeaf9e33b50d4a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5bd7947a55b72b6f6a0db88e0bd282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db8805cda07838d256165991623acca.png)
您最近一年使用:0次
2020-12-01更新
|
395次组卷
|
2卷引用:重庆市万州第二高级中学2020-2021学年高一上学期期中数学试题
10 . 若实数
、
、
满足
,则称
比
远离
.
(1)若
比
远离1且
,求实数
的取值范围;
(2)设
,其中
,求证:
比
更远离
;
(3)若
,试问:
与
哪一个更远离
,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17d41b744a89e1a50c96ca75bf090830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ea5e8fdf104e1cc8348c13a3cd1610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e00794e0df0c62a91e4b7051b2e63da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45900deae0489e87fe448948e8091c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ebc856291255f2d4a6c20b982a2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
您最近一年使用:0次
2020-07-16更新
|
1493次组卷
|
9卷引用:上海市进才中学2019-2020学年高二下学期期末数学试题
上海市进才中学2019-2020学年高二下学期期末数学试题上海市崇明区2020-2021学年高一上学期期中数学试题上海市崇明中学2021届高三上学期期中数学试题(已下线)第3章 不等式 单元综合检测(基础过关)(单元培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)专题08 一元二次函数、方程和不等式中的压轴题(二)-【尖子生专用】2021-2022学年高一数学考点培优训练(人教A版2019必修第一册)第3章 不等式(章末测试提高卷)-2021-2022学年高一数学同步单元测试定心卷(苏教版2019必修第一册)(已下线)专题02 等式与不等式(模拟练)(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列