名校
1 . 对于函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728f2cc68f8ca8ef2faa681785798259.png)
A.函数![]() ![]() |
B.![]() |
C.若方程![]() ![]() |
D.对任意正实数![]() ![]() ![]() ![]() |
您最近一年使用:0次
7日内更新
|
1311次组卷
|
2卷引用:重庆市开州中学2023-2024学年高三下学期高考模拟考试数学试题(四)
名校
解题方法
2 . 已知函数
.
(1)当
时,
恒成立,求实数
的取值范围;
(2)已知直线
是曲线
的两条切线,且直线
的斜率之积为1.
(i)记
为直线
交点的横坐标,求证:
;
(ii)若
也与曲线
相切,求
的关系式并求出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6453c2284ab370e0c3817f5e14bafa7d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43920f5171ed31db2520ef00e4c5fc24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50297ad9f7256b4d2efc3462289f18b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849df491461fb04b28fd5fe6017753e.png)
(i)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849df491461fb04b28fd5fe6017753e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f90560052fe43871fd3d594c771723c.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9849df491461fb04b28fd5fe6017753e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
3 . 对于数列
,定义
,满足
,记
,称
为由数列
生成的“
函数”.
(1)试写出“
函数”
,并求
的值;
(2)若“
函数”
,求n的最大值;
(3)记函数
,其导函数为
,证明:“
函数”
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c214af101c995038e5229277692350e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9dfaa821691b4a0f548d3a57cafb6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3862a345e98a4a34b3101bffe283be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad01b28c2aa9d86daa50de5a9fe698a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb654dbe976f077495105b21b7963d0f.png)
(1)试写出“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2837786afdd7b9b8bc37823040d7dd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167bc147c8a470e8060815303b6313a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abdb56b20415e38b25c6cc9c4319dc53.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e0c84de10f0f2186313169c3dc997b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502cb9fcc607d8622546867ccf60407f.png)
(3)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab95fa0eb7b774e15babe6854f4d8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5840bbbca91e9057cc99a5b3cd85fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb654dbe976f077495105b21b7963d0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506f4aa695eb5785abc58cf6c254c492.png)
您最近一年使用:0次
名校
4 . 已知函数
,其中e为自然对数的底数,下列选项正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99657b7b7f602075bb3bc46fe58ba90f.png)
A.若函数![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)求
的单调区间;
(2)当
时,
,求实数
的取值范围;
(3)已知数列
满足:
,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa28eec3eba6abdb9fb3374a66b2669.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343c47e107813158b6f071ab6236fe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66c815c12d9ca706826740a96f93f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73b59a36da5531dd529c1fb2e11b654.png)
您最近一年使用:0次
名校
解题方法
6 . 已知函数
.
(1)若
,求函数
在
处的切线方程;
(2)若函数
在
上单调递减,求
的取值范围;
(3)若函数
有两个极值点
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea1dae1d080a1ba5bfe1cfa4bbdfb21.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.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/d8654d4c41dcad9277be02979ffb057b.png)
您最近一年使用:0次
名校
解题方法
7 . 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
|
184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
名校
解题方法
8 . 柯西中值定理是数学的基本定理之一,在高等数学中有着广泛的应用.定理内容为:设函数
,
满足①图象在
上是一条连续不断的曲线;②在
内可导;③对
,
.则
,使得
.特别的,取
,则有:
,使得
,此情形称之为拉格朗日中值定理.
(1)设函数
满足
,其导函数
在
上单调递增,判断函数
在
的单调性并证明;
(2)若
且
,不等式
恒成立,求实数
的取值范围;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9b92a1988f20c45e8ba3887eeb6b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5b83b652a50ea15c83c826d8fb52f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a1212aca40e8dfbb97ae428c5d40a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38593523a246f9e59688f64444e0dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/584ef8a5b63c5a2a80372865ac0cc0a0.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acaa791feb147bd1a8bf5eb4f81a0cbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a4b4a9b7f0a8c3de045fe903204800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e71b49ac6c97943138bed91aab6215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d64f25e0020c3db48bb6a767afa98a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19cf16fd398ad9782cd4f5149d0c76f.png)
您最近一年使用:0次
名校
9 . 已知函数
,
.
(1)当
时,求
的单调区间;
(2)当
时,记
的极小值点为
.
(ⅰ)证明:
存在唯一零点
;
(ⅱ)求证:
.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f385b23c5ed85f350ffa395cd860f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc0733cb65fb25e9096618fff3348.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697572b42c40f498ed398099c659df1f.png)
您最近一年使用:0次
2024-05-04更新
|
264次组卷
|
2卷引用:重庆市实验外国语学校2023-2024学年高二下学期五月月考数学试题
名校
解题方法
10 . 牛顿在《流数法》一书中,给出了代数方程的一种数值解法——牛顿法.具体做法如下:如图,设r是
的根,首先选取
作为r的初始近似值,若
在点
处的切线与
轴相交于点
,称
是r的一次近似值;用
替代
重复上面的过程,得到
,称
是r的二次近似值;一直重复,可得到一列数:
.在一定精确度下,用四舍五入法取值,当
近似值相等时,该值即作为函数
的一个零点
.
,当
时,求方程
的二次近似值(保留到小数点后两位);
(2)牛顿法中蕴含了“以直代曲”的数学思想,直线常常取为曲线的切线或割线,求函数
在点
处的切线,并证明:
;
(3)若
,若关于
的方程
的两个根分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0573a6bcc480a91a43126d01bc19eeae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845b4f3a8f4aae8a8f97328dec21552a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fecaa6b3e14aaf1a20ccf2b39bbe7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b99bab533c13bb8e4d09bbc646bbb5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786213763946db2cb6974f9fabad6540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/909736dad505d81be43aef91e6309bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
(2)牛顿法中蕴含了“以直代曲”的数学思想,直线常常取为曲线的切线或割线,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfce215a0f2e0c00249cda12ac2b065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25b336a6ae4116b88076e9a9a723332.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c417b0bdd2f26b54c74c52cb763572.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11821d923a6bec96212e1cedde4244ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d93a9dc63ab7eb56073cdb154e414941.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2fd88f71f4c51c9a8249d8434258729.png)
您最近一年使用:0次
2024-04-24更新
|
752次组卷
|
3卷引用:重庆市第八中学校2024届高三下学期高考强化训练(二)数学试题