解题方法
1 . 已知函数
的最小值为2.
(1)求a的值以及f(x)的单调区间;
(2)设
,n∈N*,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce55a06cc9a35535da04ae52eb31e463.png)
(1)求a的值以及f(x)的单调区间;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ff5cb0a1f5ad74e711bd8883988a0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1278f778598dd2db64cdcd8120bfb87.png)
您最近一年使用:0次
2020-07-23更新
|
1967次组卷
|
7卷引用:河南省新乡市2020届高三年级第三次模拟考试数学(文科)试题
河南省新乡市2020届高三年级第三次模拟考试数学(文科)试题河南省新乡市2020届高三高考数学(文科)三模试题2020年普通高等学校招生全国1卷高考模拟大联考数学(文科)试题河南省部分重点高中2019-2020学年度高三高考适应性考试数学文科(已下线)专题22数列求和方法的求解策略解题模板(已下线)专题15 函数、数列、三角函数中大小比较问题(测)-2021年高三数学二轮复习讲练测(新高考版)(已下线)2021年高三数学二轮复习讲练测之测案 专题十七 函数、数列、三角函数中大小比较问题(文理通用)
解题方法
2 . 已知椭圆
的左、右焦点分别为
、
,直线
与椭圆
交于
、
两点,
,
为椭圆
上任意一点,且
的最大值为
.
(1)求椭圆
的方程;
(2)过椭圆
的上顶点
作两条不同的直线,分别交椭圆
于另一点
和
(异于
),若直线
、
的斜率之和为
,证明直线
恒过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c16eafcd77c758af3534886b1c8e365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/81ea0e7989a2709fdd0e9f89f9946d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3df14e8b1b02dbda69bfbb06269cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c748e40ba21ac5063d3bccaa57ef278.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ffc7d1af9053b027cf9e726f5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
解题方法
3 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5220c1d29955df47343122a463c46a92.png)
(1)若函数
区间
上存在极值点,求实数
的取值范围;
(2)当
时,不等式
,恒成立,求实数
的取值范围;
(3)求证:
(
,
为自然对数的底数,
……).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5220c1d29955df47343122a463c46a92.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5898e7d08ab9c447f45bc315176f6cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf0aab66798e1f60dc23c693c14e5a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f906a6300ee7f37065d38c53f259df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
您最近一年使用:0次
4 . 已知函数
各项均不相等的数列
满足
.令
.给出下列三个命题:(1)存在不少于3项的数列
使得
;(2)若数列
的通项公式为
,则
对
恒成立;(3)若数列
是等差数列,则
对
恒成立,其中真命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e115dd0cb0c28b33cdc1a43e9be779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6044fe76e20b5da7861f3d9b3f3143e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec26010780db181e89a51f780743f6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d87a9b5258b1a5eaee3b71004a4838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8fcccbb1234ad67314c96f9856e240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1a21f360eab1fb27b8cc15db4c04a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da6273df1952961f128bb340bc28e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2cc49cadf5bf94f8df8318fa7bd519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
A.(1)(2) | B.(1)(3) | C.(2)(3) | D.(1)(2)(3) |
您最近一年使用:0次
2020-11-15更新
|
1711次组卷
|
6卷引用:2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题
2019年上海市上海师范大学附属中学高三下学期第二次质量检测数学试题(已下线)数学-6月大数据精选模拟卷04(上海卷)(满分冲刺篇)上海市南洋模范中学2021届高三上学期期中数学试题(已下线)考向03 函数及其性质-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)考向15 等比数列-备战2022年高考数学一轮复习考点微专题(上海专用)上海交通大学附属中学2021-2022学年高一下学期5月线上月考数学试题
5 . 设
为正整数,区间
(其中
,
)同时满足下列两个条件:①对任意
,存在
使得
;②对任意
,存在
,使得
,其中
表示除
外的
个集合的并集.
(1)若
,判断以下两个数列是否满足条件:①
;②
?(结论不需要证明)
(2)求
的最小值;
(3)判断
是否存在最大值,若存在,求
的最大值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0740f39a899b4c789db8a66b7572df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726d53571993be48b7ffbf5c98a37626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adde1a0b0cd24c0c55da81035740161d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c423502f42e1b1cfb0a69969d6c2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b375f090c551bb2817fa942edbf9bd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b306a4f3b1a4dae4ccea356845b0020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c423502f42e1b1cfb0a69969d6c2aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30149e2b6b2a7d969bc087acba9d5f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e806ca651c85792a0b58b96566616eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d696408691dded253e6d2039107bfc8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa2648793a3889448088fa3f9f5aa49.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dfa82966d9f79b7e4d3ccff9e00322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca50deb36fe6d2c9bf0e10567a4b8a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93985c1677ba03adadbcb7df972f0fd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2020-07-16更新
|
436次组卷
|
2卷引用:上海市复旦附中2020届高三下学期期末数学试题
解题方法
6 . 已知数列
的通项公式
,
.设
,
,...,
(其中
,
)成等差数列.
(1)若
.
①当
,
,
为连续正整数时,求
的值;
②当
时,求证:
为定值;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59efda76f4efc2abd2c912495643a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0de7e144aac0a2af66d7abfbb3d1da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c5b4de1ea4b841ba07d3bc12cb0dd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68efb961550a83f5a52a4fd16917d27c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66884efff7400f92b530d69d029778d.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c44826e58f11a58d3a6c233fc5df2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/215b1424b299b737554386b090af8316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70f2244d643d2393618288de6c13e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c44826e58f11a58d3a6c233fc5df2d.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa76688cca7aa76df079c62409ac30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ea4c578d6489e453a543ead5f7d347.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
7 . 设
(
,
).
(1)若展开式中第5项与第7项的系数之比为3∶8,求k的值;
(2)设
(
),且各项系数
,
,
,…,
互不相同.现把这
个不同系数随机排成一个三角形数阵:第1列1个数,第2列2个数,…,第n列n个数.设
是第i列中的最小数,其中
,且i,
.记
的概率为
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e015379cb6580f4412dcf1fdfdc3ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c972cbd63decec197aec1bdc306de67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
(1)若展开式中第5项与第7项的系数之比为3∶8,求k的值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dbc79bfe1e18890b15a0f211b3da6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90c998886b1483221a5b4941f6e874c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b300326e522dc458655079b5dcd0a05f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d02d6bfc8f3e1c661ba2732a00a6352.png)
您最近一年使用:0次
2020-07-15更新
|
1427次组卷
|
4卷引用:江苏省南通市2020届高三下学期第四次调研测试数学试题
江苏省南通市2020届高三下学期第四次调研测试数学试题江苏省苏州市常熟中学2020届高三下学期校内适应性考试数学试题(已下线)专题9-1 概率与统计及分布列归类(理)(讲+练)-2黑龙江省哈尔滨市第三中学2021-2022学年高二上学期10月月考数学试题
名校
解题方法
8 . 已知函数
.
(1)若
且
,求
的单调区间;
(2)若
在
处取得最大值,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edea43d45e33c7760e7613ef8f8adf80.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92acace17d43431c5d414cdc3b624fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6393f6adbb2eeef1080425f58441cb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
9 . 已知函数
,
.
(Ⅰ)若
,解不等式
;
(Ⅱ)设
是函数
的四个不同的零点,问是否存在实数
,使得其三个零点成等差数列?若存在,求出所有
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e49948cb5d0925be201ed086845f1d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fcc1dbd7485c0ff2a6e1ad4d871d34.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e9fa864472349a0094a4c8328e4536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ccd22fd0ca1a8e1468329284f91b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/190a6120c3330c51d0823c8bd8991b2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-11-08更新
|
813次组卷
|
5卷引用:浙江省丽水市2018-2019学年高一下学期期末数学试题
浙江省丽水市2018-2019学年高一下学期期末数学试题广东省执信中学2019-2020学年高二上学期9月月考数学试题(已下线)【新东方】杭州新东方高中数学试卷323(已下线)第23讲 零点问题之三个零点-突破2022年新高考数学导数压轴解答题精选精练浙江省宁波市北仑中学2022-2023学年高二(1班)下学期期中数学试题
名校
解题方法
10 . 已知函数
.
(1)当
时,求函数
在点
处的切线方程.
(2)若
对任意的
恒成立,求
的值.
(3)在(2)的条件下,记
,证明:
存在唯一的极大值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b77ba7d2fd83543ff795ba95a2668b3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7d632e9ddb7d9857b073978f8314ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)在(2)的条件下,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2948d1f0476a537e7150e8a8b0d3a421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df5ea5aebfb463f9e08de0c32c1c739.png)
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2020-07-11更新
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708次组卷
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3卷引用:浙江省绍兴市柯桥区鲁迅中学2019-2020学年高二下学期期中数学试题