名校
解题方法
1 . 证明下列不等式:
(1)已知
,求证![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
,求证
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2684b72f9f38f5046c8ecd4280b7b14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead56bb8f5e7a72e9f8640e795caf68d.png)
您最近一年使用:0次
2022-10-08更新
|
243次组卷
|
2卷引用:安徽省六安市汇文中学、汇文学校2022-2023学年高一上学期第一次联考数学试题
2 . (1)已知
,证明:
;
(2)设
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e27526fad7d109f3f1e157352e5fb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7580eda2d6abb825698d18d265a7401b.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefcc738d395f255dc3518795ce597cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3b8f0a0cb7d7a8e732c33a62fdfacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f1af8d815f4b284bc0de0664bd440d.png)
您最近一年使用:0次
名校
3 . 不等式证明:
(1)已知
,求证:
;
(2)已知a,b,c均为正实数,且
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc2278547879e9246de7e749a774d7.png)
(2)已知a,b,c均为正实数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ee79d588c459ae4ca749e7b12d844b.png)
您最近一年使用:0次
名校
解题方法
4 . 选用恰当的证明方法,证明下列不等式.
(1)已知实数
,
均为正数,求证:
.
(2)已知
,
都是正数,并且
,求证:
.
(1)已知实数
![](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/5069dfceae48573f4991a1fa2f45b5c7.png)
(2)已知
![](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/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e44a6abb0974fa7a3ff0477c4e891e0.png)
您最近一年使用:0次
2021-02-06更新
|
544次组卷
|
2卷引用:江西省高安中学2020-2021学年高二上学期期末考试数学(理)试题
名校
5 . 若函数
满足:对任意实数
以及定义中任意两数
、
(
),恒有
,则称
是下凸函数.
(1)证明:函数
是下凸函数;
(2)判断
是不是下凸函数,并说明理由;
(3)若
是定义在
上的下凸函数,常数
,满足:
,
,且
,求证:
,并求
在
上的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4799629218b4b62ffa4082b96888e3c6.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/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1538a4b84a99b2da4de9600fc5552c50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6d27b23b1c41834d7516122f73f9.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45afdf4d717bb03adac6b899c367acb.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2da2ab1f8b5d3281efb94b763fa74081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9db2cae6cc39553ca2b984741630917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb4645bb34156bfc57de16ec11300f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c9a7ed0961f8977a21dab37aab396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
您最近一年使用:0次
解题方法
6 . (1)当
时,求证:
;
(2)用数学归纳法证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03425cbe241074fd29fa5bb2b1da5820.png)
(2)用数学归纳法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49a7eee6f97a8581ff245c581c672a9a.png)
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7 . 选修4-5 不等式证明选讲
已知函数
,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9e93adab0cecc867a5d2edae5fdfcd.png)
的解集不是空集.
(1)求实数
的取值集合
;
(2)若
,求证:
.
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e99852ed0dc4846cc28fbf976037ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9e93adab0cecc867a5d2edae5fdfcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f7f094e09ee6c70253de52e17816c0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf729a8a77b49347434f1b7b61ffd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63237f90bfff1b190baa80418b1b6d6d.png)
您最近一年使用:0次
8 . (1)已知a,b,x,y均为正数,求证:
并指出等号成立的条件;
(2)利用(1)的结论,求函数
的最大值,并指出取最大值时x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7381cf2d8df0ec7f569046d580d40a1f.png)
(2)利用(1)的结论,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b13d632379fbe54d0c957d1d14329e.png)
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2024-01-13更新
|
409次组卷
|
4卷引用:四川省绵阳市2024届高三二模数学(理)试题
解题方法
9 . 已知
.
(1)若
,求证:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75807858b7804a1ad2039c41f323a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288420f0b137ec90d963e6b5db65fe30.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753bc7b46730ab08df9ee4488ce34986.png)
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解题方法
10 . 设不等式
的解集为
.
(1)求证:
;
(2)试比较
与
的大小,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d5cab03c293e2c2b56e7be1bda567b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bca6fb9e5e25c0fcac557b7ea8e769e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebca3befdfa438ae6d4946cc66056af9.png)
(2)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f2a8ea6c69b9133d29a4c9060e98f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ab32d054ab39addb162a79bc872a6c.png)
您最近一年使用:0次
2023-01-18更新
|
83次组卷
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2卷引用:贵州省铜仁市2023届高三上学期期末质量监测数学(文)试题