名校
1 . 已知实数
满足
;
(1)求证:
;
(2)将上述不等式加以推广,把
的分子
改为另一个大于
的自然数
,使得
对任意的
恒成立,请加以证明;
(3)从另一角度推广,自然数
满足什么条件时,不等式
对任意
恒成立,请加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3aec1994a01be9e9335a62177131ee4.png)
(2)将上述不等式加以推广,把
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32df45c5ee591bb2b763deacb26110c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942932aac23ed64c833aacaae02e66bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
(3)从另一角度推广,自然数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b511bcbe94aa484c0a067891fbf7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3823cef58d924746e16b32155e3bc16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
您最近一年使用:0次
2020-11-12更新
|
249次组卷
|
2卷引用:上海市金山中学2020-2021学年高一上学期期中数学试题
名校
2 . 已知函数
的定义域为
,且满足:当
时,
,
、
,都有
.
(1)判断函数
的单调性并加以证明;
(2)若当
时,关于
的不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d5a0e25aebe1cc182d2247ed344652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6593a700bf3e89107556454666b787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c81b53f8bdd3a06b9753c71b55cd10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30d0fed389a86e8a6645ccd6179cef1.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503a002dd51f5338c4bc0e15fb201c3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1d82397893fe3e8d7618c4f3c4f74f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
3 . 《几何原本》中的几何代数法是以几何方法研究代数问题,这种方法是数学家处理问题的重要依据,很多代数公理、定理都可以根据这一原理实现证明,也称为“无字证明”.如图,
是圆
的直径,点
为圆心,点
是线段
上的一点,且
.过点
作垂直于
的半弦
,连接
,过点
作
垂直
于点
,则根据该图形我们可以完成的无字证明有:( )
①
②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42148a829ff0f0ebcd144d9dea83b72.png)
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34bd34d274728d23244a4e556dec936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24751374b8b7589fc7b8d78319246be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c609bf57abfc28c0b093de5a2e2ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b63d2504bd3ecce8c10560b142356f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/14/b82749b9-31c1-4a6f-a9dc-4011438263b2.png?resizew=172)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1218c73ddb7c471bedb7235ac496ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42148a829ff0f0ebcd144d9dea83b72.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9a8ee95f152e8a2bd19971057aba5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f34bd34d274728d23244a4e556dec936.png)
A.①② | B.①③ | C.②③ | D.②④ |
您最近一年使用:0次
2023-08-13更新
|
574次组卷
|
4卷引用:模块三 专题2 基本不等式的灵活运用
(已下线)模块三 专题2 基本不等式的灵活运用上海市民办文绮中学2023-2024学年高一上学期期中数学试题(已下线)模块四 专题3 题型突破篇 小题满分挑战练(4)期末终极研习室(2023-2024学年第一学期)高一人教A版陕西师范大学附属中学渭北中学2022-2023学年高二下学期5月月考文科数学试题
解题方法
4 . (1)已知x,
,
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72ac4f84da4c01b55136ff5d5d47f0e.png)
(2)已知x,
,若
,且不等式
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78cb0ce68a7d5b3704d6bd0c77fb55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72ac4f84da4c01b55136ff5d5d47f0e.png)
(2)已知x,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7324eb84ef5685b4a0fd7866858025d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d3a7a6d6857a10c1f9d30e037e467c.png)
您最近一年使用:0次
名校
5 . 已知函数
,
.
(1)判断函数
的奇偶性,并证明你的结论;
(2)若
对一切实数
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb85e8e0c2998717346b6e97543c38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b3c83e9ebea7d75e15fc2f7a7e6320.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1962bab2a0afb7924f489564192cc92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-02-03更新
|
425次组卷
|
2卷引用:江西省上饶市2022-2023学年高一上学期期末教学质量测试数学试题
名校
解题方法
6 . (1)已知
,
,
均为正数,求证:
.
(2)已知正数
,
满足
,若
恒成立,求
的取值范围.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93efa3e1b9b9ece092b3e13e6e571724.png)
(2)已知正数
![](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/a170f00dce976bcdcacd4d284e8c03de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d2c041ef33d79930983323bad00af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
7 . 已知
、
、
都是正数.
(1)求证:
;
(2)若
恒成立,求实数
的取值范围.
![](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/e81e59019989b7dc2fb59b037ef6e010.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1013644cac0113827da72373cd4c75.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff5db9f72b3fd5cc24ce5d98d68586e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2022-02-26更新
|
1076次组卷
|
7卷引用:河南省驻马店市新蔡县第一高级中学2021-2022学年高一上学期11月月考数学试题
河南省驻马店市新蔡县第一高级中学2021-2022学年高一上学期11月月考数学试题河南省名校大联考2021–2022学年高一上学期期中考试数学试题基本不等式(已下线)高一上学期第一次月考数学试卷(提高篇)-举一反三系列(已下线)2.2 基本不等式(第1课时)(分层练习)-【上好课】(已下线)高一上学期第一次月考十五大题型归纳(拔尖篇)-举一反三系列广东省广州市广州大学附中2023-2024学年高一上学期10月月考数学试题
8 . 如图,长方体
的对角线
与顶点
处的三个面所成的角分别为
.
![](https://img.xkw.com/dksih/QBM/2022/5/6/2973680760856576/2976982514958336/STEM/9f0b6e1a-d051-4d88-834d-73a904bc8ecc.png?resizew=183)
(1)证明
为定值;
(2)若
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://img.xkw.com/dksih/QBM/2022/5/6/2973680760856576/2976982514958336/STEM/9f0b6e1a-d051-4d88-834d-73a904bc8ecc.png?resizew=183)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d57a5c09b5aea68b1d8ab7ac4f750f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ca77ee1b54d7d68affb7e21d4d5c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
9 . 已知
,
.
(1)求证:
;
(2)当
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b75e17b53ee815ef4853237102ba053e.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f8b1e63af47234b235a53b07ac1e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-10-13更新
|
297次组卷
|
3卷引用:河南省豫西名校2021-2022学年高一上学期第一次联考数学试题
名校
解题方法
10 . 已知
,
,且
.
(1)若
恒成立,求
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4675bb0303560cbe552f4211d0cb32.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fbbeac6755c9eb325c068c283722a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0924c972be3ea5ecf26f803c9bb8245f.png)
您最近一年使用:0次
2022-05-09更新
|
1055次组卷
|
6卷引用:突破2.2 基本不等式(课时训练)