1 . 已知函数
,设曲线
在点
处的切线与x轴的交点为
,其中
为正实数.
(1)用
表示
;
(2)求证:对一切正整数n,
的充要条件是
;
(3)若
,记
证明数列
成等比数列,并求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7b0deaff280ebbee0f91be5acd20d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/641fec779880f75fa8ee6782f3350402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edeb4aa8a3ca0261e0161fd7fa8bde97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002f56900c2924bfd79fc3865b0a02e.png)
(2)求证:对一切正整数n,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0b3c80e774501722f46f97800f1d400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3fd5fd833041ae95d8b7f8d2897e35.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfe65f891c54780bcf1ed6a9f8a0f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
您最近一年使用:0次
2022-11-23更新
|
1076次组卷
|
3卷引用:2007年普通高等学校招生考试数学(理)试题(四川卷)
2 . 已知函数
的图象是自原点出发的一条折线,当
时,该图象是斜率为
的线段(其中正常数
),设数列
由
定义.
(1)求
和
的表达式;
(2)求
的表达式,并写出其定义域;
(3)证明:
的图象与
的图象没有横坐标大于1的交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13a0c16cb73c7381c01280f3d62a874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8212e307836cb33f16575e23f6b808e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406185f4ad8bcd99e23adc8d289088ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baf389cbaa16c0f23c6928ca31be4e52.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff60eab72de85437e12806474281612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
您最近一年使用:0次
3 . 设正项等比数列
满足
,
.令
求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853eace02560e7f1490694276c29a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057f84c7e6b5cfde2e11dd1926c50790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412d3d040e4e67daad25aa085fc45e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783af6a1ae35709a95b4287409348310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da2db7e09d2b1dbfbcd02574dae25ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b143f8888579b22c2fe7e70516310a.png)
您最近一年使用:0次
4 . 已知
是曲线
上的点,C在
处的切线
交
轴于点
,过
作
轴的垂线交C于
,C在
处的切线
交
轴于
,过
作
轴的垂线交C于点
,C在
处的切线
交
轴于
,过
作
轴的垂线交C于
,重复上述操作,依次得到
,
,……,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b088cb297522e38dff96a4b5ea600e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a098a0e65cc3a678c09ba4b90b97d91b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e367975cd9882f21334ffc8a92745161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9051c36cd615f33b0b998d098e49f0ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0235feb6050c98ad45cca7ceceaaf431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f1b40221f57567c67c1ba5ceb2f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f1b40221f57567c67c1ba5ceb2f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c57033e396170c7546b3f76e0cb5f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2d9d82c1949784452addc8047894384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92adfef6c3f4b8c041958fbf0b01f6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0269c74f81a17eca13334d53a3ae6176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82cfd620516c5812e213ed4e0534a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e056ec49e2b47361345a4db01ce788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c643b0ffd4ca67a657e04a1337faac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d94f45a4cdb64e26f49c2490aaccd8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297b6b3b19cde9602ca48acf1030e7d1.png)
您最近一年使用:0次
5 . 设
的两个根分别为
,
,设
.
(1)求证:
;
(2)求
的个位数字.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50938cb46ccd303b2d0a9faf7791adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d216801533ab2a5e3107d750de0f54e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a916f8905f8f60c36fbd8a61fd18cc70.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c523ff551d94b243e73e8e6b63a33d5.png)
您最近一年使用:0次
6 . 已知整数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe4f83589ccd37deb53db370e8e631e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ed2b042eec7bb3407d5ca5ba1220f1.png)
您最近一年使用:0次
7 . 已知数列
满足
,
,且
,
.
(1)证明:
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37f186bc71846ac158e74e58e42fdcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6194b7839446c93adc1b49aefb9d7214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f5f15f044af83e89e5f99565e612d6.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6eb5f27d859a1c31601425db58c885f.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)求函数
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ce04a52818f54d0bf8d63c822dcf.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6790f1010defae05e26f1ab6ce62f1e1.png)
您最近一年使用:0次
2022-06-06更新
|
699次组卷
|
3卷引用:吉林省吉林市普通高中2022届高三第四次调研测试理科数学试题
9 . 设复数数列
满足:
,且对任意正整数n,均有:
.若复数
对应复平面的点为
,O为坐标原点.
(1)求
的面积;
(2)求
;
(3)证明:对任意正整数m,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078c417ea54a5065c1f72941b9e4b0be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b670aca396b96eaf2c553b1ca84486dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a383b03b4869ea984d58b8d87c35402.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012d2d40a71783e79d67e7fbb01bc93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8312ce4d9e9f0aff13e64d93fbea921e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5927f1967a8f72e8fb887edb5023a921.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fec8f8ce956e4621c34db6218ed072.png)
(3)证明:对任意正整数m,均有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea99696f6df9d98c2dcc87832002874.png)
您最近一年使用:0次
10 . 已知数集
具有性质P:对任意的
,使得
成立.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)已知
,求证:
;
(3)若
,求数集A中所有元素的和的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b7edfe73bdd0bb2a6e84512b62bdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a921d157d198de0f934da07e16dc7df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e76d1341e8e6bd89b7075150536bd.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59970351aa04d29f62d480c7280763e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a3069c8accda13019e775a5dc198c2.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108bce68aab5565c4ed9a0c3e11150e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7006f52b1f7cf1bdf8374bd2da3e4562.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a94ec87afbc073e077f2c453a304b.png)
您最近一年使用:0次
2022-05-13更新
|
1010次组卷
|
7卷引用:北京市房山区2022届高三二模数学试题