解题方法
1 . 已知a,b,c为正数,且
.
(1)是否存在a,b,c,使得
?若存在,求a,b,c的值;若不存在,说明理由.
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a57e060f61f7efa54982bda67db483a.png)
(1)是否存在a,b,c,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d8406e8832ba0c8abdd9b9b4dd1945.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65186b3f16edc4e25666301b4391684.png)
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2023-05-20更新
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3卷引用:四川省大数据精准教学联盟2022-2023学年高三第二次统一监测数学(理)试题
解题方法
2 . 设函数
.
(1)当
时,求不等式
的解集;
(2)求证:对任意的
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636315156e87b47a284569633d8a4b94.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb584bbe5dbf0438934967b942521013.png)
(2)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e139ffce599f7fb165e2fd6febe6db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caeb212e8d4bdb0676c76075b446afe.png)
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2021-05-12更新
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2卷引用:四川省攀枝花市2021届高三一模考试数学(文)试题
3 . 已知数列
满足
,
.
(1)证明:数列
为等差数列;
(2)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629e54076b5754d3309da6cdcebfefc2.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25cbe66fe4e84b4022721122baab4a3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d3d55a85012933f91c5d8d27d8801d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17599b7871bea4af640acae4703f7d6.png)
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5卷引用:四川省巴中市2021届高三零诊考试数学(理)试题
四川省巴中市2021届高三零诊考试数学(理)试题(已下线)第七章 数列 专练13—证明不等式问题(大题)-2022届高三数学一轮复习(已下线)专题28 证明不等式的常见技巧-学会解题之高三数学万能解题模板【2022版】(已下线)第04讲 复习课-数列-【寒假自学课】2022年高二数学寒假精品课(苏教版2019选择性必修第二册)(已下线)专题16 数列放缩证明不等式必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
解题方法
4 . 设
,
,
,
.
(1)若
的最小值为4,求
的值;
(2)若
,证明:
或
.
![](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/c70cecfc37310dd869b0d51ff44d64e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c88f4308b66716ffe5df610b5dfb7d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93718bc80266ccc70bbdacdcad2e738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1530d6081c3fa517f04a73079ec2a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e921e4e730669eeca4baafc3b57d7a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d191d6de821fbb06a51b5a20112db6de.png)
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3卷引用:2020届四川省高三大数据精准教学第一次统一监测文科数学试题
5 . 已知函数
,且不等式
的解集为M.
(1)求
;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8e7196d17c8281cdddf97fde0a96ee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4509817be39bef4bcde115996ee39e8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879a7f6b11981ad518461614f4c37d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93300384fa7d2f5a164c8e593981459.png)
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2卷引用:【校级联考】四川省华文大教育联盟2019届高三第二次质量检测考试数学(理)试题
名校
6 . 设不等式
的解集为
.
(Ⅰ)求集合
;
(Ⅰ)若
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50dc6ffe52e2f03f79de711c05298bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅰ)求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e0c827cca31bf1ce69b52089c5b1d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91470c93fe16abb789cdb5e3a92a6fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad48b5732a02cd2f92fe0d7c451b659.png)
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