名校
解题方法
1 . 已知
,且0为
的一个极值点.
(1)求实数
的值;
(2)证明:①函数
在区间
上存在唯一零点;
②
,其中
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aaf8922b1b6e2a4366bbd142ad447b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd531902180b2316d92936e1d1c5219d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f759e5772fb6972efa066f9d0ea363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
您最近一年使用:0次
2023-03-24更新
|
3430次组卷
|
9卷引用:湖北省武汉市武昌区2022-2023学年高二下学期期末数学试题
湖北省武汉市武昌区2022-2023学年高二下学期期末数学试题山东省烟台市2023届高三一模数学试题山东省德州市2023届高考一模数学试题专题07导数及其应用(解答题)江苏省南京市临江高级中学2023届高三下学期二模拉练数学试题广东省深圳市福田区红岭中学2023届高三第五次统一考数学试题四川省宜宾市叙州区第一中学校2023-2024学年高三上学期10月月考数学(理)试题(已下线)重难点突破09 函数零点问题的综合应用(八大题型)(已下线)第九章 导数与三角函数的联袂 专题四 利用导数证明含三角函数的不等式 微点1 利用导数证明含三角函数的不等式(一)
2 . 设数列
的前n项和为
,已知
,
,
,若
,则正整数k的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c840b24a1626f247eefe7371c8abb50e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2889dd3096379db5dfdd51305bdbb743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2bba93ea41b19a10e9c791029f254c4.png)
A.2016 | B.2017 | C.2018 | D.2019 |
您最近一年使用:0次
3 . 已知数列
满足
,
,令
,设数列
前n项和为
.
(1)求证:数列
为等差数列;
(2)若存在
,使不等式
成立,求实数
的取值范围;
(3)设正项数列
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8363902560fce392e05042b7287929a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacbbf38ec1b411cfd9693874bebd4a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5fc0b571e6545e133d36af338733b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb3185977be193745f403547d1e9800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8261beeefacd521644faf4658227a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)设正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d1dbbe083e1e1672b2439ea746d976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf47abf4f5649d379a8a69983a3fc56.png)
您最近一年使用:0次
2022-07-21更新
|
1594次组卷
|
7卷引用:四川省眉山市2021-2022学年高一下学期期末数学(理)试题
四川省眉山市2021-2022学年高一下学期期末数学(理)试题广东省广东实验中学2023届高三上学期第一次段考数学试题(已下线)4.2.3 等差数列的前n项和-2022-2023学年高二数学《基础·重点·难点 》全面题型高分突破(苏教版2019选择性必修第一册)(已下线)4.2.2.2 等差数列的前n项和的性质及应用(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)专题15 数列不等式的证明 微点6 数列不等式的证明综合训练(已下线)数列与不等式(已下线)4.1 等差数列(第2课时)(十三大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
4 . 英国数学家泰勒发现了如下公式:
,其中
,此公式有广泛的用途,例如利用公式得到一些不等式:当
时,
,
.
(1)证明:当
时,
;
(2)设
,若区间
满足当
定义域为
时,值域也为
,则称为
的“和谐区间”.
(i)
时,
是否存在“和谐区间”?若存在,求出
的所有“和谐区间”,若不存在,请说明理由;
(ii)
时,
是否存在“和谐区间”?若存在,求出
的所有“和谐区间”,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c8d6b7790572ee26dac80e0c7fe648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ee051a4daa81ab32ef9c153ecf90e02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305249d05ecc23ee86ae55f7bf8566e1.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9f80e45170c557aed6187a6bd11177d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f95d2a9ba5f50d14cdee5ecda28461a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0db2c49919467a2e14540f2aabd05cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2022-02-22更新
|
1537次组卷
|
5卷引用:福建省福州第一中学2021-2022学年高一上学期期末考试数学试题
福建省福州第一中学2021-2022学年高一上学期期末考试数学试题(已下线)专题09 导数压轴解答题(证明类)-12024届高三新改革适应性模拟训练数学试卷七(九省联考题型)辽宁省实验中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题11 利用泰勒展开式证明不等式【练】
名校
5 . 设函数
.
(1)求函数
的单调区间;
(2)若关于x的方程
有两个不相等的实数根
、
,当
时,证明:
.(注:
…是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603589540f7897790f99a8d75fd725f9.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5809a06357f94fc7a2156c7e7af1ed2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b741ffe4fcf3227685a7439071c66c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1cf765d06d182c85b65daa5f55fd07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a35e5501b2700f624bd4a9144fc9ec.png)
您最近一年使用:0次
2022-01-21更新
|
774次组卷
|
2卷引用:浙江省宁波市慈溪市2021-2022学年高三上学期期末数学试题
6 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedd7be672b179eaf072f53635fe130b.png)
_____ ;若直线
(
)与函数
的图象有交点,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd0690b529099376398a467c9c0612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aedd7be672b179eaf072f53635fe130b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46111e4d12c21798aa213c0d7804c2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd0690b529099376398a467c9c0612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
7 . 已知函数
.
(1)证明:
时,
;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9a6a0ad0a5ee53205ac42a6261fa03.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b9a926eb1876d017ce1198e32efec6.png)
您最近一年使用:0次
2020-12-14更新
|
1693次组卷
|
7卷引用:江苏省苏州市张家港市2022-2023学年高三上学期1月期末数学试题
江苏省苏州市张家港市2022-2023学年高三上学期1月期末数学试题安徽省池州市东至县2020-2021学年高三上学期12月大联考数学(文)试题安徽省全省名校实验班2020-2021学年高三上学期大联考文科数学试题(已下线)专题04 利用导数证明不等式 第一篇 热点、难点突破篇(讲)- 2021年高考二轮复习讲练测(浙江专用)(已下线)专题15 函数、数列、三角函数中大小比较问题(讲)-2021年高三数学二轮复习讲练测 (新高考版)(已下线)专题04 利用导数证明不等式(讲)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)第三章 重点专攻二 不等式的证明问题(讲)
解题方法
8 . 已知数列
满足
.
(1)求数列
的通项;
(2)设
,若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53c811b8b0124c799580b5fa9cae3929.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980d51ba3340a31964fbec9e6f243ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcbc64b0f3d08d5285ee32e5ca13d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e6afc5de00034c4b65e5c2841c1e299.png)
您最近一年使用:0次
解题方法
9 . 已知数列
满足
,
(
),数列
的前n项和为
,且满足
(
).
(1)求数列
,
的通项公式;
(2) 记
, 求证:
①当n≥2且
时,
;
②当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e7fdd39f7b10edcbd53ac0ec2b56ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1714ada78260c1c1c93689ca98aed151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2) 记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
①当n≥2且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427af291f810f5ac3a23b926c121408c.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74437f0f50e8f69bc2da22fa2795d146.png)
您最近一年使用:0次
解题方法
10 . 已知正项数列
满足
,
.
(1)试比较
与
的大小,并说明理由;
(2)设数列
的前
项和为
,证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2474d6d9f5f9cddc8e7e34485ee62cf.png)
(1)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95cc577a6d59b2c5ca7916af2b7b492.png)
您最近一年使用:0次