解题方法
1 . 对于数列
,若存在
,使得对任意
,总有
,则称
为“有界变差数列”.
(1)若各项均为正数的等比数列
为有界变差数列,求其公比q的取值范围;
(2)若数列
满足
,且
,证明:
是有界变差数列;
(3)若
,
均为有界变差数列,且
,证明:
是有界变差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b12bed9580c9e3efaaae3f234780cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若各项均为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b22febb1e578366695d7628740370bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7c13436fc942bddb9c562520fb855a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc883e0a2ee951e94f305c807e66010a.png)
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名校
解题方法
2 . 已知
,且
.
(1)解关于
的不等式:
;
(2)求证:对任意
恒有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
(1)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976738081afc41550f88aca83861c1b4.png)
(2)求证:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8deae40c582f0759f3d01acb1c0c6c.png)
您最近一年使用:0次
2023-03-30更新
|
336次组卷
|
3卷引用:贵州省2023届高三考前备考指导解压卷数学(理)试题
解题方法
3 . 已知函数
,
的表达式分别为
,
,
.
(1)证明:函数
在区间
上是严格增函数;
(2)求函数
的最小值及相应
的取值集合;
(3)若函数
,
且
对一切
恒成立,则称
的图像在
的图像的上方.求证:当
时,
的图像在
的图像的上方.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75f46f632f2a710b3617f69c3d31ba00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cac43c22b4da6e232f4891d71f0bbb5.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d133cf04971ea0116f2f54982f4e92b.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83f3574c440135b1e8d33f9662e7e883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b197c6e77b06afde23727f9f498e9ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442958bd5b5f8ac690b33ea0bccdd0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
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4 . 对于数列
,
,其中
,对任意正整数
都有
,则称数列
为数列
的“接近数列”.已知
为数列
的“接近数列”,且
,
.
(1)若
(
是正整数),求
,
,
,
的值;
(2)若
(
是正整数),是否存在
(
是正整数),使得
,如果存在,请求出
的最小值,如果不存在,请说明理由;
(3)若
为无穷等差数列,公差为
,求证:数列
为等差数列的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78393519255d80cb3c118a0d71f15511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4719086a4e785f6b5fdb429a313ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20c7b6daa1896a8a274c53f78562987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26617babc02c5fcd7f26963a39d63bcd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce6549c5171680493c49b60b7556e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a548938d87c80ac47910607d3857007f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390a3ae2949dfbf5a342bda3372d3149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ba29be0a4f589c51de211609728ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf4973ccdd9289ee99369aaa916cb6c.png)
您最近一年使用:0次
2022-12-16更新
|
693次组卷
|
3卷引用:上海市徐汇区2023届高三一模数学试题
5 . 设a、b为不相等的实数,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877c0be40ec541ed3b403a5917f615cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19000de5a7a0437c5fe7aae9cf713787.png)
您最近一年使用:0次