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1 . (1)已知
,用比较法证明:
;
(2)已知
,用基本不等式证明:
,并注明等号成立条件;
(3)已知
,用反证法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2128a00f52af4427721f0ebba591daa.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a521891098b625f372ff648d110afe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d66530037e9ad08b11dfe515571f41.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937559aeec06323cde8861b17024fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be100015cff38b6dfba5080fa94d128.png)
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解题方法
2 . 已知正数a,b满足
.
(1)求
的最小值;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f82faec003c719363cfee623d410b.png)
不小于25.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f00f997ae12c30f551adb834e1d7ef8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219ba6c8a1b54598db1a78cab28d9d30.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f82faec003c719363cfee623d410b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
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3 . 命题“已知
,若
且
,则
”,判断命题的真假,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
![](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/6d0403068265fb3323a37cae4228b201.png)
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解题方法
4 . 在
中,
、
、
分别是角
、
、
所对的边,
是
、
的等差中项,则
与
的大小关系是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1810555c0c28fe352841322b85bbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18436f0e2391b0ab7537a566fc28204c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-08-12更新
|
669次组卷
|
3卷引用:上海市松江一中2022届高三下学期3月阶段测试数学试题
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5 . 设
,
,则“
”是“
”的( )
![](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/095b82ba973150118a0689f63e17dd42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5144df368bcbdeb5c1870c5675608b71.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分又不必要条件 |
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2022-05-08更新
|
1508次组卷
|
5卷引用:上海市七宝中学2022-2023学年高一上学期10月月考数学试题
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解题方法
6 . 已知
,且
,求证:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49f899086e636caaed2075a2c7b924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0050f60381c11bd08745623096f0a66e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128294be1f10b83df30ad60d4c696224.png)
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7 . 已知
,且
,则下列不等式中不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fca18a32677dfe9ed27365a9f658e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5f0d374837655cc286d326305da36.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知a、b、c是互不相等的正实数.
(1)若a、b、c成等差数列,求证:
、
、
不可能是等比数列;
(2)设
的三内角A、B、C所对边分别为a、b、c,若
、
、
成等差数列,求证
.
(1)若a、b、c成等差数列,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cbec06c8cb9891ac12e28d29414d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b04b385894ad75674a418c21b3b861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed30faca453723a2ffbe21a0dafb9ee.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c70fcaa661df4fbcad820b439accda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9237dbe3a4f28962ef2870b4e7dab599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26302e47e2926b0e807952b0efe7463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc74ad5dbb6029f4bd4ea0d52f576945.png)
您最近一年使用:0次
2021-10-18更新
|
372次组卷
|
2卷引用:上海市进才中学2022届高三上学期10月月考数学试题
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解题方法
9 . 已知
为正实数,利用平均不等式证明(1)(2)并指出等号成立条件,然后解决(3)中的实际问题.
(1)请根据基本不等式
(
),证明:
;
(2)请利用(1)的结论,证明:
;
(3)如图,将边长为1米的正方形硬纸板,在它的四个角各减去一个小正方形后,在这层一个无盖纸盒.如果要使制作的盒子容积最大,那么剪去的小正方形的边长应为多少米?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
(1)请根据基本不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689f982af451283289255c87593ec338.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c270c7508ec18bfae26af47763aab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e17f1b7e916807416bb2941b0788fe7.png)
(2)请利用(1)的结论,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c169995b2eaa06bef72f45dc41f134ce.png)
(3)如图,将边长为1米的正方形硬纸板,在它的四个角各减去一个小正方形后,在这层一个无盖纸盒.如果要使制作的盒子容积最大,那么剪去的小正方形的边长应为多少米?
![](https://img.xkw.com/dksih/QBM/2021/9/21/2812835216646144/2814555843821568/STEM/e4a74bf0-8094-45d2-886c-d915171dc433.png?resizew=532)
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10 . 对于函数
,若对任意
,均有
,则称此函数为下凸函数,试证明函数
是下凸函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cf3765e5650555113994da8771e3e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc1bc250c8a6523a1be394ff48d4a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a7901661c71b40b5601ad0c0f6dacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d17c3dfbe1a448fd6747dcd1879941e.png)
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