名校
解题方法
1 . 定义在
上的函数
满足
,
(若
,则
,
为常数),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c0a028f1d7bffc087f345909ddbb498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4915a7b17389ab1238077f4c4ee8f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b61ce28ace610a80435c2806c85502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() ![]() ![]() |
B.![]() |
C.若![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
2023-02-09更新
|
595次组卷
|
5卷引用:河北省沧州市2023届高三上学期12月教学质量监测调研数学试题
河北省沧州市2023届高三上学期12月教学质量监测调研数学试题吉林省长春市第六中学2022-2023学年高二下学期4月月考数学试题吉林省长春市南关区实验中学2022-2023学年高二下学期期末数学试题(已下线)高二下学期第一次月考数学试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)(已下线)高二下学期期末数学试卷(提高篇)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)
名校
解题方法
2 . 已知数列
中,
,且
,若存在正整数
,使得
成立,则实数
的取值范围为( )
![](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/53ca2cae224aae175d07a96cf95c9118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551b1fb748642c8e6b3deced91340b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-09更新
|
1152次组卷
|
2卷引用:河北省沧州市2023届高三上学期12月教学质量监测调研数学试题
名校
3 . 已知
,其中
,且函数
为奇函数;
(1)若函数
的图像过点
,求
的值域;
(2)设函数
,若对任意
,总存在唯一的
使得
成立,求实数
的范围;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654d85458441482b7cf5a3471e716675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26927f1f0be044942dfce30c3607158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7b4be1c7d881d9386085dc41c416e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d93adfe763e2b7589f85ac34d1fa9d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2c920ddd6649a9c254fd186803d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2492d486aef92677bc4d9c88c28b6845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)若
,求
在
处的切线方程.
(2)是否存在实数
,使
对
恒成立?若存在,求出
的值或取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2eac2ca815b49d08974e3811d62b56.png)
(1)若
![](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/9b384412acba251d87902ab928902f16.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e077e2b54bc477d571c47b8cc5923b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.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
5 . 已知椭圆
的短轴长为2,点
在
上.
(1)求
的方程;
(2)设
是
上不同于短轴端点
(
点在
点上方)的两点,直线
与直线
的斜率分别为
,且满足
,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59a1d3e6a94f1bcea354d37318fd003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279563c3c055777ce1aa369a2ef54aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d8707cafd80cde5c561e2b5a3531c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2378c56a66f5b2d80cc814df0804210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
解题方法
6 . 设
,
,
,那么以下正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e76dc48811f2e4fb01ab9d4dd31e4c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994e021ce5c75238889c1d0f716036dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc6a77d616d75921b42cb65c6eb6c00.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知一动圆与圆
外切,与圆
内切,该动圆的圆心的轨迹为曲线
.
(1)求曲线
的方程.
(2)已知点
在曲线
上,斜率为
的直线
与曲线
交于
两点(异于点
).记直线
和直线
的斜率分别为
,
,从下面①、②、③中选取两个作为已知条件,证明另外一个成立.
①
;②
;③
.
注:若选择不同的组合分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334eced457d4ba4b994fb8f90073a026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a195b6d605a528ae425ba2d641c1dbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8115c09f801cf0bb02293baef7bf137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d200a411fbc2f50ad72f1fd729a7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71471908991617852f8b27bceeb689cd.png)
注:若选择不同的组合分别解答,则按第一个解答计分.
您最近一年使用:0次
2023-01-05更新
|
1268次组卷
|
3卷引用:河北省张家口市2022-2023学年高二上学期期末数学试题
解题方法
8 . 已知函数
.
(1)当
时,求函数
的极值;
(2)若函数
有两个不同的零点
且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f86bbfe670c9e7f3efb5d4ac622141.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416d7fee68d59f36198065ab2cb97586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8144cab892ddd789f64b282b4e3c4bc3.png)
您最近一年使用:0次
名校
9 . 已知函数
.
(1)若
,求
的单调区间;
(2)记函数
,若
恒成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2101148669e4d91bfcbb50ecaeeda959.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d88b062b915f661ed2e3e2dabd8f7648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90cf4872dc05f4c5d6e99bdb363668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9acfcfee22e0a4128ee72e96721f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-11-28更新
|
454次组卷
|
4卷引用:河北省冀东名校2022-2023学年高三上学期期中调研考试数学试题
河北省冀东名校2022-2023学年高三上学期期中调研考试数学试题(已下线)大题强化训练(10)(已下线)考点19 导数的应用--函数零点问题 2024届高考数学考点总动员新疆维吾尔自治区乌鲁木齐市第十一中学2024届高三下学期开学考试数学试题
名校
解题方法
10 . 设
为
的导函数,若
是定义域为
的增函数,则称
为
上的“凹函数”.已知函数
为R上的凹函数.
(1)求
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156b7d51065e1d0188d6b2780970cac7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35c8f0d5e9348e6cf9f9ff4a300382b.png)
您最近一年使用:0次
2022-11-26更新
|
341次组卷
|
4卷引用:河北省2023届高三上学期11月联考数学试题