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解题方法
1 . (1)求证:当
,
,
为正数时,
;
(2)已知
,
,求证
.
![](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/077ed1711b7328d5c4e3b3f2e63f6ba1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e43d45156e16bb5a3f702255b1f8ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50074b38ef831a2bec2c73c1bc5268a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d46fe93b8aa8efcc4c0f072db6f63f5.png)
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2 . 不等式证明:
(1)证明不等式:
(其中
皆为正数)
(2)已知
,
,
,求证:
至少有一个小于2.
(1)证明不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fbd934eef4b3b38cb981b60cc0af6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.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/69bbd0aae5a4f6129fc78f88f662f092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3b7d1702786875b9984fe517fa1360.png)
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2020-03-19更新
|
833次组卷
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3卷引用:陕西省西安中学2017-2018学年高二(实验班)下学期期中数学(理)试题
陕西省西安中学2017-2018学年高二(实验班)下学期期中数学(理)试题河南省南阳华龙高级中学2019-2020学年高二5月月考数学(文)试题(已下线)2.2.2 间接证明-2020-2021学年高二数学(理)课时同步练(人教A版选修2-2)
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3 . 已知数列
的各项均为正数,
,且对任意
,都有
,数列
前n项的和
.
(1)若数列
是等比数列,求
的值和
;
(2)若数列
是等差数列,求
和
的关系式;
(3)
,当
时,求证:
是一个常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52eaeadb3e8b1123dc482d1b947fba21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abd1fa09bdb402d8f67a00407708fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf34fbe2923b70a5312ef24748bc51c4.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c7aab4df25884973273efae244f2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c5b850ab7d16794ca7f520170a4f32.png)
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4 . △ABC的三个内角A,B,C成等差数列,A,B,C的对边分别为a,b,c.
求证:
.
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043714f337a44c343813c4e34f699211.png)
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5 . 已知
,
,且
,用分析法证明
![](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/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b336fad1a2ecd1a87f5af4c80b25db5b.png)
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6 . 用分析法证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d502b65ae46819f35344430f1dd9bc.png)
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2019-06-02更新
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2卷引用:【校级联考】福建省宁德市高中同心顺联盟校2018-2019学年高二下学期期中考试数学(文)试题
7 . 计算:
,
;所以
;又计算:
,
,
;所以
,
.
(1)分析以上结论,试写出一个一般性的命题;
(2)判断该命题的真假.若为真,请用分析法给出证明;若为假,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab60bf2cd96c89716535d287e1e5730e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a2de18918df4f06f29c232b3543a32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98cdb98805ab4a51d5edf97c4d11f3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65fd510988ced5d7eca08a3d8f651571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422bb31d9be2f6b89945034eadd8b90c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1c69852c24e97cdb26b40408827d0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3792d738e15382ea8f910b42531273b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec4fd1e621825718bdf99d31a631624b.png)
(1)分析以上结论,试写出一个一般性的命题;
(2)判断该命题的真假.若为真,请用分析法给出证明;若为假,请说明理由.
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2019-05-24更新
|
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2卷引用:【校级联考】福建省三明市三地三校2018-2019学年高二下学期期中联考数学(文)试题
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8 . 已知
,
,
均为正实数.
![](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)
(Ⅰ)用分析法证明:≤
;
(Ⅱ)用综合法证明:若=1,则
≥8.
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3卷引用:【全国百强校】安徽省马鞍山二中2018-2019学年高二第二学期期中素质测试(理)数学试题
9 . 已知:
;
;
.
通过观察上述三个等式的规律,写出能反映一般规律的等式,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175c6d4e6bea4498e433d6910807a70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea616295fe9501f5059a6fbe5aa3306a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2db2081507b58d706a5fe54f931942.png)
通过观察上述三个等式的规律,写出能反映一般规律的等式,并证明你的结论.
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2018高三上·全国·专题练习
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10 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3348778fd42e9d895afdbc088c7044e8.png)
.
(1)若函数
在
上是增函数,求正数
的取值范围;
(2)当
时,设函数
的图象与x轴的交点为
,
,曲线
在
,
两点处的切线斜率分别为
,
,求证:
+![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3348778fd42e9d895afdbc088c7044e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb49dbba01c4ff5f686ffc8828351b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/51c530f4b7491b95acb8ce3eef9aa09d.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/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37708a68d0ca72413ada85d01d2ed19.png)
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2018-12-12更新
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10卷引用:2019年3月24日 《每日一题》理数选修2-2-每周一测
(已下线)2019年3月24日 《每日一题》理数选修2-2-每周一测重庆大学城第一中学校2018-2019学年高二下学期第一次月考数学(理)试题重庆市第三十七中学校2018-2019学年高二下学期期中(理)数学试题河南省郸城第二高级中学2019-2020学年高二下学期网上学习数学(一)理科试题吉林省梅河口市第五中学2019-2020学年高二4月月考数学(文)试题甘肃省武威第一中学2019-2020学年高二下学期期中考试数学(理)试题河南省洛阳市豫西名校2020-2021学年高二下学期第一次联考文科数学试题(已下线)2018年12月12日 《每日一题》一轮复习【文】-直接证明与间接证明(已下线)2018年12月11日 《每日一题》一轮复习【理】-直接证明与间接证明甘肃省庆阳市华池县第一中学2022-2023学年高一下学期期中数学试题