2024高三·全国·专题练习
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1 . 已知实数a,b,c满足
.
(1)若
,求证:
;
(2)若a,b,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25863514e359f6c6feabfd1477c815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28512b04591f079d997d4e675394585.png)
(2)若a,b,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829bdd79ab193cdd707c537b72f19251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a5b6a23f530bddc0b3b4ea826df429.png)
您最近一年使用:0次
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2 . 阿基米德有这样一句流传很久的名言:“给我一个支点,我就能撬起整个地球!”这句话说的便是杠杆原理,即“动力×动力臂=阻力×阻力臂”.现有一商店使用两臂不等长的天平称黄金,一位顾客到店里购买
黄金,售货员先将
的砝码放在天平左盘中,取出
黄金放在天平右盘中使天平平衡;再将
的砝码放在天平右盘中,取
黄金放在天平左盘中使天平平衡,最后将称得的黄金交给顾客,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0304ceec0e725588194fa1de44f9a50e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12af1d28d48a91afd098444706128b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c5a64c9ecc0fc05a332456cc510d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12af1d28d48a91afd098444706128b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b2d30a4556a157b89f2f88ebc57cefe.png)
A.![]() | B.![]() | C.![]() | D.以上选项都有可能 |
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2024-03-31更新
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2卷引用:四川省仁寿第一中学校南校区2023-2024学年高一下学期入学考试数学试题
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3 . 已知数列
为等差数列,
为等比数列,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98506c2c0e51ae8e57900246c93f8b5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:四川省南充市第一中学2023-2024学年高三下学期4月月考数学试题
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解题方法
4 . 设
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a525e811ffc32387348f431b04c32225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce243be426caee3afd136c7c47f3e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa65fbb04bade6da52b633edf66b7b8.png)
A.![]() | B.![]() | C.![]() | D.无法确定 |
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2卷引用: 四川省什邡中学2023-2024学年高二下学期期中考试数学试题
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解题方法
5 . 已知正实数
,
,
满足
.
(1)若
,证明:
.
(2)求
的最大值.
![](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/71dd40d3df2762d6e6bdefcb5f397269.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e370bb90fbd819d76b005145819a8838.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818daf1a57c4b4c3666d411dcc76f8a.png)
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3卷引用:四川省雅安市雅安中学等校联考2023-2024学年高三下学期开学考试数学(文)试题
6 . 已知
,则下列不等关系正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 以下说法正确的有( )
A.实数![]() ![]() |
B.![]() ![]() |
C.命题“![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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8 . 下列结论正确的是( )
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() ![]() | D.若![]() ![]() |
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解题方法
9 . 已知
,
,且
,证明:
(1)
;
(2)
.
![](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/5be97cd1c7111b654d87d8fbb63b6a84.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fac5d2ab1b9171b01c57f18ad9d65b2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ed49c9f3dd88de817f0ab422e961d35.png)
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10 . 已知函数
,
.
(1)证明:对任意
,
,都有
.
(2)已知
,设
是函数
的零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61f35cc9cbb97d3fed21c28d3ade436f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
(1)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a7901661c71b40b5601ad0c0f6dacc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f60d84eefeb29aa178963d2660c3a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6a25791c334b8b79ee02c03a73e693.png)
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2023-11-30更新
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