名校
解题方法
1 . 已知函数
是定义域为
的奇函数,且满足
.
(1)判断函数
在区间
上的单调性,并用定义证明;
(2)已知
,
,且
,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0968841c3b9731f5fe1308f9dc7c5023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2e0f3d6270d6cd9dd35956b05c574f4.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03db4ea1dcb63b22cf4e917df5db581e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1a5699410baa270f3fa8153ab346e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
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2 . 已知
,
为正数,证明下列不等式成立:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa23408bcc9f6200f22a310e5f2569a.png)
(2)
(其中
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa23408bcc9f6200f22a310e5f2569a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2b7ea83c42b08f7fa98f40b7ceb797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
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3 . (1)已知
且
,证明:
,并指出何时取到等号;
(2)已知
,证明:
,并指出何时取到等号.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf04fe8895c10624636a815d3d752975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ed2296215d64f2df2cedc608a10dc61.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ee6696dee035519e1ba7fb78269830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05cc9795ebfd58c83164204b163261ea.png)
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解题方法
4 . 已知正数a,b满足
;
(1)求ab的最大值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d34836cf6d21bcadd4f60793ba150.png)
(1)求ab的最大值;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296a77a7ca3e70fba643654bf5a99a3b.png)
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2023-10-12更新
|
359次组卷
|
5卷引用:陕西省部分学校2023-2024学年高一上学期10月选科调考数学试题
5 . 已知实数
满足
.
(1)证明:“
”是“
”的充要条件;
(2)若
且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
(1)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7191888571b035030e43e1ff327117b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33ac81a1325ac63e1c01968f35773be.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d31b8c91a07e3cab110256c92c0fd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8d507b9f264f7bd72cf0a6a964291a.png)
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6 . 已知
,
.
(1)若
,证明:
.
(2)若
,求
的最小值.
(3)若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2feac7a3eaffd79d927bad4a572b5173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ea0bf27de07b4699b1a5abee1ed7ff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b155b33772898966d74d5eb0084df56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3b9cf82c01d09dacc4d1ce888652b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3910a0f217d8109b9467f740fc84a73d.png)
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名校
7 . (1)已知
,求
的取值范围;
(2)设a,b,c均为正数,且
,证明:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afba78f1ed058a450f2f74665ad7b150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd927b4b5a7875528c1b54aa4bb8b2dd.png)
(2)设a,b,c均为正数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d689b0da0bd4803b3e8a6c69542ae466.png)
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解题方法
8 . (1)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
且
,求
的最小值.
(2)已知
,
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2a9344f4fca7b9779ca7720e5277ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c915b4ce31fabfd4703c547291ad9277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86db1ff1b996e33de049889c04bf9a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd31dc2d0967db352574381d66d33fc0.png)
(2)已知
![](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/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054d00a127a585f7401a05d5351c6e37.png)
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名校
9 . 若正数a,b,c满足
.
(1)求
的最大值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0818daf1a57c4b4c3666d411dcc76f8a.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e41caf7d9fe70feb99f10b5c9dc423.png)
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2023-04-24更新
|
1019次组卷
|
7卷引用:河北省石家庄市十五中2022-2023学年高一下学期第一次月考数学试题
河北省石家庄市十五中2022-2023学年高一下学期第一次月考数学试题(已下线)第二章:一元二次函数、方程和不等式章末综合检测卷-【题型分类归纳】(已下线)专题2.7 一元二次函数、方程和不等式全章综合测试卷(提高篇)-举一反三系列湖南省长沙市第一中学2023-2024学年高一上学期第一次阶段性检测数学试题(已下线)模块一 专题2 一元二次函数、方程和不等式1(人教A)湖北省武汉市水果湖高级中学2023-2024学年高一上学期10月月考数学试题(已下线)专题04 基本不等式压轴题-【常考压轴题】
10 . (1)设
均为正数,且
,证明:若
,则
:
(2)已知
为正数,且满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eeda5cef4846ef829069fe27f64e34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34913253db59e64279ca78cfdd5f1569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef0e9d305e0fc426a0425911e54ea21.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3681a97ebef383e8968347548102fb49.png)
您最近一年使用:0次