1 . 已知函数
.
(1)求证:
在
上有唯一的极大值点;
(2)若
恒成立,求a的值;
(3)求证:函数
有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e36f6875b53680483500331a87f338.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c225b4e4c6a628296fc60354163a8e60.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/361f7fc6f387c880147685c65ec91705.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a20457d180264f78d611dc7893d735.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
2 . 已知双曲线E:
的一条渐近线为
,左顶点为A,右焦点为
,点B,C是双曲线E的右支上相异的两点,直线AB,AC分别与直线l:
交于M,N两点,且以线段MN为直径的圆恰过点F.
(1)求双曲线E的标准方程.
(2)求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b650820d7bed48ed67a2869ad8c65ff1.png)
(1)求双曲线E的标准方程.
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
3 . 已知
,函数
的图象在点
处的切线方程为
.
(1)求a,b的值;
(2)若方程
(e为自然对数的底数)有两个实数根
,且
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba240aef63c1a33b764ff8f8f54b68fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49446ac763a93a2573eb3d4edd56770.png)
(1)求a,b的值;
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f79440ba25d4ae21f3e30ad14642bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8a42225463cf3abb26bcbcf7d5e440e.png)
您最近一年使用:0次
4 . 已知双曲线
:
的渐近线为
,焦距为
,直线
与
的右支及渐近线的交点自上至下依次为
、
、
、
.
(1)求
的方程;
(2)证明:
;
(3)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10273b05ad8210d8db07639c4d149fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/8455657dde27aabe6adb7b188e031c11.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1af14f9a53cb0f07d5d28dceba30aa.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/571664dafc35f8c9ee5cc20eebc80c9a.png)
您最近一年使用:0次
2024-04-29更新
|
777次组卷
|
2卷引用:湖南省长郡中学、浙江省杭州二中、江苏省南京师大附中三校2023-2024学年高三下学期联考数学试题
2024·全国·模拟预测
5 . 已知函数
,
.
(1)讨论
的单调性;
(2)设
,若
存在两个不同的零点
,
,且
.
(i)证明:
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab77f55f79cee8544a7ab77cb24d2df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a9bebf693fb74fa2facc183e2befee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.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/26d8dafc71b106f39f4e15442220897b.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e56a3e34af7ead94132148603541b8d.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a57c53cbf56d5496ac4a7a49e82047b5.png)
您最近一年使用:0次
2024·全国·模拟预测
6 . 已知函数
.
(1)若
,讨论
的单调性.
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b375522a04f97b8cd95b6127788bb81a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862b42ff6ab277a6089f8a6f67597a2b.png)
您最近一年使用:0次
7 . 设函数
,
.
(1)求函数
的单调区间;
(2)若总存在两条直线和曲线
与
都相切,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b21c310a00732a9eda5489e225bd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa761dc81ad0c9ae739ef627867bd0c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47661347486366d63f8b2f7225651a5a.png)
(2)若总存在两条直线和曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
8 . 英国数学家泰勒发现了如下公式:
,其中
,e为自然对数的底数,
.以上公式称为泰勒公式.根据以上信息,并结合高中所学的数学知识,解决如下问题:
(1)证明:当
时,
;
(2)证明:对任意的正整数
;
(3)证明:e是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48350c9f896c18a64f27867ca81c9be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e510e333b7dcc02f3f763eed7174fae9.png)
(2)证明:对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c15c55fc99e9b54eb6a797e5bc5b7e.png)
(3)证明:e是无理数.
您最近一年使用:0次
2024·全国·模拟预测
解题方法
9 . 英国数学家泰勒发现了如下公式:
,其中
,
为自然对数的底数,
.以上公式称为泰勒公式.设
,
,根据以上信息,并结合高中所学的数学知识,解决如下问题:
(1)证明:
;
(2)设
,证明:
;
(3)设实数
使得
对
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068fe824048360fba77109636452fda8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b302cf413a9ca1b05ab584a023cfbd.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d84ae7f43ef85da907d2917ff5f2a80.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebbb26aaeaedb2a77bc826a9d1dcfe3.png)
(3)设实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a54ecefd96e1a86d32ff0a82bc048d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
10 . 已知曲线
在点
处的切线为
.
(1)求直线
的方程;
(2)证明:除点
外,曲线
在直线
的下方;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1026c00ff9d78946b4984d09de77995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f84134092f31767ff9f7e8200a79fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:除点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa83d5be9b28fcfce25c9bfca0d3d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab873c4173a3992c043fbf32cab4d8c.png)
您最近一年使用:0次
2024-04-26更新
|
1268次组卷
|
4卷引用:安徽省合肥市2024届高三第二次教学质量检测数学试卷