名校
解题方法
1 . 已知函数
,
且
.
(1)若
恒成立,求实数a的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16919057eaa179ace514abc614032fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665dc334a37e61c356b636604eb0f8c3.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2729c6cc5a733a1218698c4e745f5df.png)
您最近一年使用:0次
2023-02-25更新
|
207次组卷
|
2卷引用:河南省名校联盟2023届高三大联考(2月)文科数学试题
名校
解题方法
2 . 已知函数
.
(1)求
的最小值
;
(2)若
为正实数,且
,证明不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeac9c68cb0927860b9501715aee4161.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4437f0a5f10a9ff9fe6b7d6d353f67c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdedd395cdf9ce33624a1dd9439d41ea.png)
您最近一年使用:0次
2023-05-03更新
|
669次组卷
|
6卷引用:江西省重点中学盟校2023届高三第二次联考数学(文)试题
名校
解题方法
3 . (1)设x、y是不全为零的实数,试比较
与
的大小,并说明理由;
(2)求证:
对所有实数x恒成立,并求等号成立时x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf877c2f179cf4e47657882ee8fa14d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ecbb4dc189112b811b31483f2aa695.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb49a6dbbe8fe0ca51e4cc915855ae81.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)若
,解不等式
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c9ccc8ef54ca5f66b9eb1258dd2d25.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb4d6744a7fceeb92b8d49099cd69f07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f883787bfaef0505db49fe1694d63f12.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dc308242af3bb293bd9e3422b9f6f5c.png)
您最近一年使用:0次
2022-04-19更新
|
332次组卷
|
3卷引用:湘赣皖长郡十五校联盟2022届高三第二次联考(全国卷)文科数学试题
解题方法
5 . 已知函数
.
(1)若
,且
,求
的取值范围;
(2)若
在
上有零点,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd340af8d33b00f72394d033e04856e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e65a4c62cceb75d2b85e136c38da08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b446bc19f96fab880012a3d053b4bdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b246aa3b56becc905d3fb64c6d5ec4a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2999b8725bda6436940bdbaf51109da5.png)
您最近一年使用:0次
6 . 已知函数
(
).
(1)若
,求证:
;
(2)若对于任意
,都有
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b670eca949fe38c0a092e8f00a7d816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ea2fe6d047bc6d2c13ff4d397e8508.png)
(2)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a349161b52f9493112280309454cd9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc42c1dcd2d8574feaacb9ac2829c078.png)
您最近一年使用:0次
2022-03-13更新
|
429次组卷
|
4卷引用:中学生标准学术能力诊断性测试2022届高三3月测试数学文科试题
名校
解题方法
7 . 已知函数
.
(1)求函数
的最小值;
(2)若
时,证明:对任意的
,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6536be62e96caf85e5bc68ec4870e2ac.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f184ef9e0d57554e95f369c9d4bbfea1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90918b116ddc7dd7115ece5520dbd006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34a735097182a079267f2bc97b9940.png)
您最近一年使用:0次
2022-04-01更新
|
502次组卷
|
6卷引用:青桐鸣2021-2022学年高三3月质量检测理科数学试题
8 . 已知函数
(
).
(1)若
,
,求
的值域;
(2)若
,当
时,
的最大值为
,求
的值;
(3)当
时,记
最大值为
,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3ae10a087e083b6b8158ec6f5e78ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773ca22fc12ade9e60dbc749ba5cfa73.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86304c3e26200299a0480641525a283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365114c53aa12abda1004c8e4cb4ca0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4333157b51f440ab416ed20fcbf405f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365114c53aa12abda1004c8e4cb4ca0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a676af21ca9c25f86ce5f55cb4e9443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0600e01e00fa3d34e3cb3cba46314207.png)
您最近一年使用:0次
20-21高三下·河南·阶段练习
解题方法
9 . 设不等式
的解集为
.
(1)求集合
;
(2)设
是
中元素的最大值,正数
,
,
,
满足
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8a3b8f12417907ec8fc738db5d909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9048a4655708ea1ff6702b4b5061975a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7324eb84ef5685b4a0fd7866858025d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd6ab858cb89df63e44633517aea5b7.png)
您最近一年使用:0次
20-21高三下·全国·阶段练习
解题方法
10 . 已知函数
.
(1)解不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353c51e38c33301e335ab3a5344d9e1c.png)
(2)记不等式解集
中元素数值最小值为
,若正实数
满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a469a8db0a0a4acef31c074d61cb17b8.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353c51e38c33301e335ab3a5344d9e1c.png)
(2)记不等式解集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/353c51e38c33301e335ab3a5344d9e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9a8ddeb83566685cf31c319bd0484b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6dfad6c2e8d19daeb93beb5e336163e.png)
您最近一年使用:0次