1 . 在平面直角坐标系
中,
的直角顶点
在
轴上,另一个顶点
在函数
图象上
(1)当顶点
在
轴上方时,求
以
轴为旋转轴,边
和边
旋转一周形成的面所围成的几何体的体积的最大值;
(2)已知函数
,关于
的方程
有两个不等实根![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
.
(i)求实数
的取值范围;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815191eaa8a97bc63eb83cb11df51ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804af6e0fde82f2192cec6061257e4dd.png)
(1)当顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815191eaa8a97bc63eb83cb11df51ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558d3298c715c7f293dadebab3108fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f88653ab06d6f3fa74fff528b0255c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af029e933ded38d74c2a9d283e3b92d3.png)
(i)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cbb53ad7f80fcd5326bf9cf488b2a4b.png)
您最近一年使用:0次
解题方法
2 . 已知函数
(e是自然对数的底数),
.
(1)若函数
,求函数
在
上的最大值.
(2)若函数
的图象与直线
有且仅有三个公共点,公共点横坐标的最大值为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976581d4a974fe50f9f29d430c1289f2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a34d46575f388984a69d1660ab8667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b426608a06477f57cb994f4d00e4465d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3331dd8cf4127ffdb2e541115dc118a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082990da1f11a1a7be4fc3935c0d526e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ec8eb92402d57af55813b15578e86c.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)求函数
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ce04a52818f54d0bf8d63c822dcf.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6790f1010defae05e26f1ab6ce62f1e1.png)
您最近一年使用:0次
2022-06-06更新
|
699次组卷
|
3卷引用:吉林省吉林市2022届高三第四次调研测试数学(理)试题
名校
解题方法
4 . 已知函数
.
(1)证明:函数
的图象与直线
只有一个公共点;
(2)证明:对任意的
,
;
(3)若
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7159e60d2b9d109b2543eb6aba7071e1.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(2)证明:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a89210cf3fda807166c5f03e9831b8.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3516c9df36097a79027e380e40e3a0ad.png)
您最近一年使用:0次
2022-11-10更新
|
316次组卷
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2卷引用:吉林省吉林市吉化第一高级中学校2022-2023学年高三上学期12月月考数学试题
名校
5 . 已知函数
.
(1)讨论
在
上的单调性;
(2)若
,证明:函数
在
上有且仅有三个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8a40dc05978ed607ffa4cefa5a9834.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b765f8ca3ad399fd309d3d6cbab856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
您最近一年使用:0次
2022-05-07更新
|
351次组卷
|
4卷引用:吉林省吉林市第一中学2021-2022学年高二6月月考数学试题(理科创新班)
吉林省吉林市第一中学2021-2022学年高二6月月考数学试题(理科创新班)河南省豫西名校2021-2022学年高三下学期4月教学质量检测文科数学试题(已下线)文科数学-2022年高考考前20天终极冲刺攻略(四)(6月5日)安徽省阜阳市临泉第一中学2022-2023学年高三上学期期中数学试题
6 . 已知
.
(Ⅰ)对一切
恒成立,求实数
的取值范围;
(Ⅱ)当
时,求函数
在区间
上的最值;
(Ⅲ)证明:对一切
,都有
成立.
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/efb71d4162564ed898738b882d7468a6.png?resizew=196)
(Ⅰ)对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ebfc2f77a9668796f1af76729430321.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/c503ce16f1a04fa2be68c15a7ddfb234.png?resizew=12)
(Ⅱ)当
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/eef680bbdd144eccb118ead4e9f762e8.png?resizew=40)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/bb67b510a28d43b882b27b9275575666.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/47fef5e308ef47eda626bf7fc82e3468.png?resizew=108)
(Ⅲ)证明:对一切
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/c020059c99e94b33af0614411f3c924b.png?resizew=76)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470528032768/1572470533849088/STEM/ae357641c5dc4213a7ceb3059cfea31a.png?resizew=113)
您最近一年使用:0次
名校
解题方法
7 . 函数
,其图象与
轴交于
,
两点,且
.
(1)求
的取值范围;
(2)证明:
(
为
的导函数).
(3)设点
在函数
图象上,且
为等腰直角三角形,记
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e15f2f74fba6a77b73e1fc059ae90de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2086e2e0fef338f69cf29237efb9e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f90045c2bac484d4a65223accdc47d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133c30d6ca96a4d8de293da20fbe8f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a73f6325db462bf8e4471ae7fcb2544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90212f1ea6290f2ae947b47bed84ccbd.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d889069ca94e0339f85b84ce01047943.png)
(1)若
,试讨论
的单调性;
(2)若
,实数
为方程
的两不等实根,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d889069ca94e0339f85b84ce01047943.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826156c89739a80927f7eae7dab5328a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cecf79d95aa74776e7889f3d4c16589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1dce6b38a62408d78e4c8b632be0d6d.png)
您最近一年使用:0次
2020-04-18更新
|
1041次组卷
|
6卷引用:2020届吉林省吉林市高三第三次调研测试(4月) 数学(理)试题
2020届吉林省吉林市高三第三次调研测试(4月) 数学(理)试题辽宁省辽河油田第二高级中学2020届高三6月模拟考试数学(理)试题(已下线)专题21同构、罗必塔法则、隐零点、双变量等问题(讲)(理科)第一篇 热点、难点突破篇-《2022年高考理科数学二轮复习讲练测》(全国课标版)(已下线)第五章 导数及其应用(选拔卷)-【单元测试】2021-2022学年高二数学尖子生选拔卷(苏教版2019选择性必修第一册)(已下线)专题35 导数中双变量与极值点偏移必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)湖北省仙桃市田家炳实验高级中学2022-2023学年高三上学期9月月考数学试题