1 . (1)用综合法证明:
,
,
均为正实数);
(2)已知:
,
,
,求证:
,
中至少有一个不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cfb2a3446d8011b89d87fba03a20e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d6b6b86228a9b721d618fae2963e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd86a39ae4fb080287cda63e4a68266.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/c95b6be4554f03bf496092f1acdfbb89.png)
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2 . ①已知
,
是实数,若
,则
且
,用反证法证明时,可假设
且
;②设
为实数,
,求证
与
中至少有一个不少于
,用反证法证明时,可假设
,且
.则
![](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/2eb5374855bb495fafbdace1c47e492a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406185f4ad8bcd99e23adc8d289088ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb74c6813d470dd2943f709d025c227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdd18f831934fb27cc00e4642ba7cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637495a71588804f786b9787e8095dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65962ee028d986a30fd87206d891a154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176b1438fbfc1855c0b5e161da854874.png)
A.①的假设正确,②的假设错误 | B.①的假设错误,②的假设正确 |
C.①与②的假设都错误 | D.①与②的假设都正确 |
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2018-05-02更新
|
410次组卷
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3卷引用:【全国市级联考】河南省焦作市2017-2018学年高二下学期期中考试理科数学试题
3 . 已知:
,
是正实数.求证:
与
不可能相等.
![](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/16f0b84ee4ed90face0993d4f4dda379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2696d72704a8274a995063527e89d38f.png)
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4 . 试写出直线与平面平行的判定定理并证明.(证明过程包括已知、求证和证明)
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5 . 用反证法证明“三角形的三个内角中至少有一个不大于
”时的假设为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
A.三个内角中至多有一个不大于![]() | B.三个内角中至少有两个不大于![]() |
C.三个内角都不大于![]() | D.三个内角都大于![]() |
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2018-04-29更新
|
371次组卷
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2卷引用:【全国市级联考】山西省太原市2017-2018学年高二下学期阶段性测评(期中)数学理试题
6 . 用反证法证明“a,b,c三个实数中最多只有一个是正数”,下列假设中正确的是( )
A.有两个数是正数 | B.这三个数都是正数 |
C.至少有两个数是负数 | D.至少有两个数是正数 |
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2014-12-22更新
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6卷引用:【全国百强校】吉林省长春市第十一高中2018-2019学年高二上学期期末考试数学(理)试题
7 . (1)已知a、b、c是不全相等的正数,且
.求证:
.
(2)用反证法证明:若函数
在区间
上是增函数,则方程
在区间
上至多只有一个实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa54caec3efb5765d189b06789c336ad.png)
(2)用反证法证明:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
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8 . 设
,
,
,
大于0,则4个数
,
,
,
的值( )
![](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/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ecc3aaae2aa289591a3b632f1e0645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45a8e3c0c4510ae1e7752a6ddc3dcce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d82444c50f8b4e9e2653457ca4d1d83.png)
A.至多有一个不大于1 | B.都大于1 |
C.至少有一个不大于1 | D.都小于1 |
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2020-10-11更新
|
138次组卷
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2卷引用:贵州省毕节市威宁县2019-2020学年高二下学期期末考试数学(文)试题
9 . 用反证法证明命题“三角形内角中至多有一个钝角”,假设正确的是
A.假设三个内角都是锐角 | B.假设三个内角都是钝角 |
C.假设三个内角中至少有两个钝角 | D.假设三个内角中至少有两个锐角 |
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10 . 用反证法证明命题:“已知
.
,若
不能被7整除,则
与
都不能被7整除”时,假设的内容应为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2a39beea5adf5d07aea0424ca7a64f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7943d48bb7efae04239914196024ae22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fbb116f99eccab7f825bdabb70bb73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2a39beea5adf5d07aea0424ca7a64f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/581c04af30b490da1a50555f9c89125c.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2017-03-06更新
|
543次组卷
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5卷引用:2016-2017学年山东省胶州市普通高中高二上学期期末考试数学(文)试卷