名校
解题方法
1 . 已知函数
.
(1)求函数
的最小值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ae309841b3cffa828d8b1537f6ed81.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c7914c666a4e4dc6a0ff76f01c47d6.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程:
(2)若
恒成立,求实数
的取值范围;
(3)证明:
(
,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6326d0794c9e7eb511e0be733ce09114.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4a9b57fc3a19a572c2959a7004fe7d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5479b9a3456d44b5fabdf6a408569fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb8d099cabd8b3578b00abbf80e37f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
您最近一年使用:0次
2024-01-31更新
|
1813次组卷
|
3卷引用:辽宁省沈阳市第二中学2024届高三下学期开学考试数学试题
解题方法
3 . 已知函数
.
(1)求曲线
在点
处的切线与两坐标轴围成的三角形的面积;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d03d40c4ac2b406cf26e33f97bce7a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c0f1ae6cc4d1c16fee1fc90473150e.png)
您最近一年使用:0次
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ed07b0ce942687ba7a87c997a7b767.png)
(1)讨论函数
的单调性;
(2)若
,证明:
,
.(提示:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ed07b0ce942687ba7a87c997a7b767.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc55062abcda348cb4cf9837e2ab936d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad5c8a4e4bad474651c0a61de820ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aaa7db4b6344ee1bc22e47e4c760533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe8be09d4ab0e414d110e09ee20e3df.png)
您最近一年使用:0次
2023-10-12更新
|
154次组卷
|
2卷引用:辽宁省朝阳市名校联考2023-2024学年高三上学期开学数学试题
名校
解题方法
5 . 已知函数
.
(1)当
时,
恒成立,求实数
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec74022c3d20a1e7017e84920f30cfd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8291ca77106b0bcd3de09a4b9e63504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1dd548055a06de23bf929f6eb1896d1.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
.
(1)求证:
;
(2)若
,试比较
与
的大小;
(3)若
,问
是否恒成立?若恒成立,求
的取值范围; 若不恒成立,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc7a277581319a8a8257ab3ce84cf0b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257e0a13428a004a923b59d092cf77de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22165fb1166b885fec563eb95b778882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f01e03edfbc7ad3ffd890fd0e682458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-05-30更新
|
657次组卷
|
2卷引用:辽宁省沈阳市第二十中学2023-2024学年高三上学期第一次模拟考试数学试题
7 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)证明:(1)中的切线经过定点;
(3)若
在
上有极值,求
的取值范围,并指出该极值是极大值还是极小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53daab2363fb6fa8c5753da2ea15e0f9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)证明:(1)中的切线经过定点;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-10-12更新
|
360次组卷
|
3卷引用:辽宁省朝阳市名校联考2023-2024学年高三上学期开学数学试题
名校
8 . 设方程
有三个实数根
.
(1)求
的取值范围;
(2)请在以下两个问题中任选一个进行作答,注意选的序号不同,该题得分不同.若选①则该小问满分4分,若选②则该小问满分9分.
①证明:
;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b513d7bdd17b6ead5295a0400d0ab15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2755e84aeb379e0117e278f71ca0a9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)请在以下两个问题中任选一个进行作答,注意选的序号不同,该题得分不同.若选①则该小问满分4分,若选②则该小问满分9分.
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5600c61eb9170becdd342ee5619d412d.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af8a6b51796f510821931ea6a9d9cc50.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,且
.
(1)求实数
的取值范围;
(2)设
为整数,且对任意正整数
,不等式
恒成立,求
的最小值;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0097e221a2fd7333fb0d47e86546ba61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2b790c0ffe766b815ea769920bf5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac9ea10cc95de77e1a0ad091359e590.png)
您最近一年使用:0次
2023-05-14更新
|
645次组卷
|
4卷引用:辽宁省六校2023-2024学年高三上学期期初考试数学试题
名校
解题方法
10 . 已知函数
.
(1)当
时,求
在区间
上的最值;
(2)若
有两个不同的零点
,
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e9f45f86ee4cac88d16435393c7cec.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b448fe164c2c2931805e3b3847dcdd75.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29909a4fdb8764b59f28bb63ce8da9db.png)
您最近一年使用:0次
2023-07-14更新
|
543次组卷
|
4卷引用:辽宁省锦州市渤海大学附属高级中学2023-2024学年高三下学期2月摸底考试数学试题