名校
解题方法
1 . 若函数
在定义域内存在两个不同的数
,同时满足
,且
在点
处的切线斜率相同,则称
为“切合函数”
(1)证明:
为“切合函数”;
(2)若
为“切合函数”,并设满足条件的两个数为
.
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbcc25bee0bd3ceeb3e8d0573f34b6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87b4c3b6486ddc142457f3781d898d8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a5ca0a482b48b476356bf5e2c502810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a0b39ed179340810fea23d244406ce.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65885209eb867c87729188328ae03261.png)
您最近一年使用:0次
2024-05-12更新
|
190次组卷
|
2卷引用:重庆市名校联盟2023-2024学年高三下学期第一次联考数学试题
2 . 已知函数
(a为常数).
(1)求函数
的单调区间;
(2)若存在两个不相等的正数
,
满足
,求证:
.
(3)若
有两个零点
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa8ea75ca2f775085b1838bef2c641d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若存在两个不相等的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3da00fe1feafb42d7e2254dd5f8589.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c67a34394380636fdf4b882ce28d40.png)
您最近一年使用:0次
2023-12-30更新
|
1241次组卷
|
10卷引用:黑龙江省哈尔滨市第六中学校2022-2023学年高三上学期期中数学试题
黑龙江省哈尔滨市第六中学校2022-2023学年高三上学期期中数学试题福建省宁德市福安市福安一中2023-2024学年高三上学期10月月考数学试题(已下线)模块三 大招24 对数平均不等式(已下线)模块三 大招10 对数平均不等式重庆缙云教育联盟2024届高三高考第一次诊断性检测数学试卷(已下线)模块五 专题6 全真拔高模拟6(已下线)模块2专题7 对数均值不等式 巧妙解决双变量练(已下线)专题6 导数与零点偏移【练】(已下线)专题16 对数平均不等式及其应用【讲】(已下线)5.3 导数在研究函数中的应用(练习)-高二数学同步精品课堂(苏教版2019选择性必修第一册)
名校
3 . 已知函数
,曲线
在点
处的切线为
.
(1)求
的方程;
(2)判断曲线
与直线
的公共点个数,并证明;
(3)若
,令
,求证:对任意的
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47bdd7fa866c56bf4fc60ad7f369db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9f8845aa2b51c460f2d798c9f62fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)判断曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3682822ac42a9c9196109af27044b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d1d8e655e9989b888fbab8099690eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852913f3c6048e49f9ccd2b6fee57eda.png)
您最近一年使用:0次
4 . 已知:平面内的动点P到定点为
和定直线
距离之比为
,
(1)求动点P的轨迹曲线C的方程;
(2)若直线
与曲线C的交点为M,N,点
,
当满足 a 时,求证: b .
①
;
②
;
③直线
过定点,并求定点的坐标.
④直线
的斜率是定值,并求出定值.
请在①②里选择一个填在a处,在③④里选择一个填在b处,构成一个真命题,在答题卡上陈述你的命题,并证明你的命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求动点P的轨迹曲线C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315a24a74c99dfa18e6d8b1b5220724b.png)
当满足 a 时,求证: b .
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/123a37d2688c0db395c86167f7fb9a52.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4808dca4874ae8142a91ce5605f9d7b.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
请在①②里选择一个填在a处,在③④里选择一个填在b处,构成一个真命题,在答题卡上陈述你的命题,并证明你的命题
您最近一年使用:0次
名校
解题方法
5 . 在无穷数列
中,若对任意的
,都存在
,使得
,则称
为m阶等差数列.在正项无穷数列
中,若对任意的
,都存在
,使得
,则称
为m阶等比数列.
(1)若数列
为1阶等比数列,
,
,求
的通项公式及前n项的和;
(2)若数列
为m阶等差数列,求证:
为m阶等比数列;
(3)若数列
既是m阶等差数列,又是
阶等差数列,证明:
是等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57ae28a9ca230ff60fff6406b06ba96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd2c3166d0bfd9e64bdc85081445e95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8483c0e1d0daabfa8130baa9737eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/674f03ad5f8c00ce301ecb176fb23277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25fe433dbc540279bc50cf65c7f5fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec50a8616d7700de94ee53c2b5dac43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec50a8616d7700de94ee53c2b5dac43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
您最近一年使用:0次
2024-05-31更新
|
362次组卷
|
3卷引用:山东省淄博实验中学2024届高三下学期第三次模拟考试数学试题
名校
解题方法
6 . 已知数列
:
,
,…,
.如果数列
:
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba977bedd76ef240d07fde83894bbe8.png)
满足
,
,其中
,则称
为
的“衍生数列”.
(1)若数列
:
,
,
,
的“衍生数列”是
:5,
,7,2,求
;
(2)若
为偶数,且
的“衍生数列”是
,证明:
的“衍生数列”是
;
(3)若
为奇数,且
的“衍生数列”是
,
的“衍生数列”是
,…依次将数列
,
,
,…第
(
)项取出,构成数列
:
,
,
….求证:
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.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/8ba977bedd76ef240d07fde83894bbe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d7e6327ecd86c682863f4a89e619fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da65bfc5919df189631c53048808e4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0171d0cea7070a6536e0c756b6907e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a821e643d5fae24caed0faa6d423dad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f5c583c98a1fd516c6ceaa60b55dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452b9bcf720355d0678d62cbf6857ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1602c6064af12eed3fd1291f8272d93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93f4ddebf0e34a5c3e9232ae66709aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/452b9bcf720355d0678d62cbf6857ffe.png)
您最近一年使用:0次
2023-11-23更新
|
451次组卷
|
4卷引用:北京市汇文中学2023-2024学年高三上学期期中考试数学试题
北京市汇文中学2023-2024学年高三上学期期中考试数学试题(已下线)压轴题数列新定义题(九省联考第19题模式)练(已下线)黄金卷06宁夏回族自治区2023-2024学年高二上学期期末测试数学训练卷(二)(范围:选择性必修第一册 第三章+选择性必修第二册 第四章)
名校
解题方法
7 . 已知数列
的前
项积为
,且
.
(1)求证:数列
是等差数列;
(2)证明:
.
![](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/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3406df6552d66166d04a3d22e2f86929.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a40442811c08c432ec613102e4502c0.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031efafb3886a33f3ac39fc85eab869d.png)
您最近一年使用:0次
2023-10-13更新
|
1988次组卷
|
4卷引用:江苏省南京市江宁区东山高级中学三校联考2023-2024学年高三上学期期中调研考试数学试题
江苏省南京市江宁区东山高级中学三校联考2023-2024学年高三上学期期中调研考试数学试题江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省连云港市部分学校2023-2024学年高三上学期10月第二次学情检测数学试题
8 . 已知函数
.
(1)讨论函数
在
上的单调性;
(2)当
时,
①判断函数
的零点个数,并证明.
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eea8ddadb910710765fb78ca1696c10b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c6b9fa72109ba69163a5c6b7874a2.png)
①判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1350cb142ba647b1a96ed5d7063665.png)
您最近一年使用:0次
9 . 已知数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
是否是等比数列?若是,给出证明;否则,请说明理由;
(2)若数列
的前10项和为361,记
,数列
的前n项和为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390636a89883bd64bf8da9bf8654aff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060c880252326cb449d8253539d92aff.png)
(1)判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf33b2a94eae16760d746f9b4b8dbc.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04053ecf80b3bb9179c8baab47bf8dae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc0cf1f0a00718b95a2a4fffd11dd32.png)
您最近一年使用:0次
2023-08-20更新
|
2550次组卷
|
9卷引用:山东省济宁市泗水县2024届高三上学期期中数学试题
解题方法
10 . 已知函数
.
(1)若
,求证:
.
(2)讨论函数
的极值;
(3)已知
,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62a17669c88f983c5d3da9138a9db55.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0155265d7c6452a7773de26a3cb66a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211e655e16740f33849b82e059b42d0d.png)
您最近一年使用:0次