名校
解题方法
1 . 已知定义在
的严格增函数
与
.若对任意实数
,存在实数
和
,不等式
恒成立,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa311daf7a73f8c45de4462f9d92b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302cf658af80ec14f1828b3727e7a511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8578c6d7d390a36d1728070bbd9cc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365114c53aa12abda1004c8e4cb4ca0c.png)
![](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/c1eb1ef0bb8706a483144babfc03a655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-13更新
|
358次组卷
|
3卷引用:上海市五爱高级中学2023-2024学年高一上学期期末考试数学试卷
解题方法
2 . 已知函数
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
时,求
的单调区间;
(2)若
与
在
上的单调区间和单调性相同,试探究方程
的实根的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85218920bb3682c9f8a5c38f05d3c489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ff40dec77111a73a00cf084883a293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a215072a06d124b82e3aae30a5e34fb5.png)
您最近一年使用:0次
解题方法
3 . 对于函数
及正实数
,若存在
,对任意的
,
恒成立,则称函数
具有性质
.
(1)判断函数
是否具有性质
?并说明理由;
(2)已知函数
具有性质
,求实数
的取值范围;
(3)如果存在唯一的一对实数
与
,使函数
具有性质
,求正实数
的取值情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cf3765e5650555113994da8771e3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b80225b1c0e43c14d90ee75f50f9817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5cc7b3d2601cd882e374f38df5e254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326452bda2f207bbb661b4e805fd7f59.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a3b559d22b7ab01ecd87e99a5fdb01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9beb2fb34710397280c318e5392e19f.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20be954eb33ebab545112d07e04c794b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714efc5adfb2e2910fb190a299215bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)如果存在唯一的一对实数
![](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/2bb2c1e778d749382c00d0cca83cfb71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/326452bda2f207bbb661b4e805fd7f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2022-01-24更新
|
333次组卷
|
2卷引用:上海市闵行区2021-2022学年高一上学期期末数学试题
名校
4 . 设函数
,
,其中
.若
恒成立,则当
取得最小值时,
的值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05183fca410df27fc3d69d61bd526486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf322b61457bd0bd7484b4349f537e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
2020-05-25更新
|
437次组卷
|
4卷引用:2020届江苏省徐州市高三上学期第一次质量抽测数学试题
2020届江苏省徐州市高三上学期第一次质量抽测数学试题2020届江苏省苏北四市(徐州、宿迁、淮安、连云港)高三上学期期末数学试题江苏省扬州中学2019-2020学年高三下学期4月月考数学试题(已下线)专题3-4 压轴小题导数技巧:多元变量(多参) -2
5 . 已知a,
,且
,若对
,不等式
恒成立,则
的最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a140256a925272cb5aae2584ac17ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d3830bb0297088943207142509169a.png)
A.![]() | B.![]() | C.1 | D.![]() |
您最近一年使用:0次
名校
6 . 已知
是定义在
上的函数,记
,
的最大值为
.若存在
,满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3572457f6eb45b5d49138da4cd0d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec65b538f7ba2d5f636623ee85955e2.png)
,则称一次函数
是
的“逼近函数”,此时的
称为
在
上的“逼近确界”.
(1)验证:
是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc04a40b5a7fd2504316a164190beeb.png)
的“逼近函数”;
(2)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f906bab9959325ca0d2dd54b57786bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7a3dbf513ce40befb25a801e6cf7a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7316f2f1cf67a610e31adfa12ef50d6d.png)
.若
是
的“逼近函数”,求
的值;
(3)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f906bab9959325ca0d2dd54b57786bb0.png)
的逼近确界为
,求证:对任意常数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1291ecd1ed0c05219d47f05fb585bd52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cd32efb968fbe9782f556ba6e5ae99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3b73875f5ded5e57738d7575f085b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3572457f6eb45b5d49138da4cd0d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec65b538f7ba2d5f636623ee85955e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bfa3b19dbc87544ec8e57606cb067d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d8a4cf957865fad1cb648fcd2cbaa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
(1)验证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4b0eba587d0af5c665a8f909df5104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc04a40b5a7fd2504316a164190beeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f906bab9959325ca0d2dd54b57786bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7a3dbf513ce40befb25a801e6cf7a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7316f2f1cf67a610e31adfa12ef50d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/106e346ccfc716b38eba9e2404a5ea8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e136e7637543c8ae92c8dcd55b31924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f906bab9959325ca0d2dd54b57786bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc868a2077000982bd4594d95cfc351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba58ee96c397a0e865e5ec333a664bb.png)
您最近一年使用:0次
2020-01-30更新
|
330次组卷
|
5卷引用:上海市川沙中学2021-2022学年高二下学期期末数学试题
上海市川沙中学2021-2022学年高二下学期期末数学试题(已下线)上海高二下学期期末真题精选(压轴60题35个考点专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)2017届上海市浦东新区高考三模数学试题2017届上海市浦东新区高三下学期5月练习数学试题上海市南汇中学2024届高三上学期期中数学试题
名校
解题方法
7 . 已知函数
若关于
的方程
有且仅有两个不同的整数解,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de287e591ee8a8704facb30ac07de131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979725d4b754614feb5c8522ad9bf24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-05-06更新
|
1743次组卷
|
6卷引用:黑龙江省大庆实验中学2021-2022学年高二实验一部下学期期末考试数学试题
黑龙江省大庆实验中学2021-2022学年高二实验一部下学期期末考试数学试题【区级联考】天津市南开区2019届高三第二学期模拟考试(二)数学(理)试题2019届天津市南开区高三高考二模数学(文)试题浙江省金华市曙光学校2019-2020学年高一下学期第一次月考数学试题(已下线)数学-6月大数据精选模拟卷01(天津卷)(满分冲刺篇)(已下线)第13题 含绝对值方程根的个数问题(压轴小题)