1 . (1)设
,
,求证:
;
(2)已知
,
,且
.证明:
或
.
![](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/54d8bf9316bb1dfb0559333ce56b35a6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e131cdd242d56b6dba05ab3363ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8e5b510c343f9d3d626fa1a4b36bad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36ffaf917dcebc8719f2ca539a774ec.png)
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2 . 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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3 . (1)
为实数,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f25298d03745e6d91799449ed9e96a.png)
(2)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f25298d03745e6d91799449ed9e96a.png)
(2)用分析法证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b492c09f576ab6491af4848ce7ecec4.png)
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4 . 证明:
是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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5 . 下列结论中正确的是( )
A.若幂函数![]() ![]() ![]() |
B.若函数![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若幂函数![]() ![]() ![]() |
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2023-10-10更新
|
758次组卷
|
3卷引用:福建省泉州市泉州科技中学2023-2024学年高一上学期期中数学试题
6 . (1)若
,证明:
.
(2)已知
,
,
,
,试证明a,b,c至少有一个不小于1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b162ff5b8a1ca4b0e934dbb1b2fed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3513efc9a14792e1fe9fa3ff5888d396.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cab560cdc1f2fff8483e64235774d2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512670a2a8ffebb9ca69d4b75ec16de1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033e0d9d0fcdfde98da36c30556ce240.png)
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7 . 观察下列不等式的规律:
,
,
,
…
请你通过上式猜测第
个不等式,并用分析法加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba13715296ed0fb8369a2a94b06adf86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77713b5f4d95699d5076586ebb9ac532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/758bd7510461dcefa6e1e56f678ed2bf.png)
…
请你通过上式猜测第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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2023-08-14更新
|
51次组卷
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2卷引用:云南省昆明市第一中学2023-2024学年高一上学期入学考试数学试题
2022高一·全国·专题练习
名校
8 . 已知
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09506fb301b62b82e8ce6b5eaf9c988f.png)
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2023-05-23更新
|
258次组卷
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3卷引用:专题2.1 等式性质与不等式性质-重难点题型精讲-2022-2023学年高一数学举一反三系列(人教A版2019必修第一册)
(已下线)专题2.1 等式性质与不等式性质-重难点题型精讲-2022-2023学年高一数学举一反三系列(人教A版2019必修第一册)广东省佛山市顺德市李兆基中学2023-2024学年高一上学期10月月考数学试题青海省海南藏族自治州高级中学2022-2023学年高二下学期期末考试数学(文)试题
2022高一·全国·专题练习
9 . 证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead56bb8f5e7a72e9f8640e795caf68d.png)
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10 . 选用恰当的方法证明下列不等式
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679e658fa5679ce73e1b5fdfe434b724.png)
(2)已知
,证明:
.
(3)已知a,b,c均为正实数,求证:若
,则
.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679e658fa5679ce73e1b5fdfe434b724.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa4f85f4d4f4bd9edaa8a964565ca1a.png)
(3)已知a,b,c均为正实数,求证:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a57e060f61f7efa54982bda67db483a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d54c9eb01acfe09c34cb808326cc5e.png)
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