名校
1 . 下列不等式中正确的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:2024届河南省名校联盟考前模拟大联考三模数学试题
2 . 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)
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2024-04-29更新
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3 . 已知
,函数
,
.
(1)求函数
的单调区间和极值;
(2)设
较小的零点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7024cf60d3372f97899a7087cec0e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c11a11eae6199342d2d0fc671c43e70.png)
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2023-02-15更新
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3卷引用:浙江省十校联盟2023届高三下学期2月第三次联考数学试题
2021·全国·模拟预测
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解题方法
4 . 设函数
.
(1)求函数
的单调区间;
(2)若函数
有两个不同的零点
,
,
为
的导函数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98452a45746410926fa3ab006338854e.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e737b076dbc720db3030a7efb84e8e.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/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b91118c18ef731302a7a54f33702bf.png)
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5 . 已知a>0,函数f(x)=2eax﹣x,若函数
恰有两个零点,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e1757c1276f928619c9378259a5b9d.png)
A.[![]() ![]() | B.(0,![]() | C.(0,![]() | D.[![]() ![]() |
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6 . 已知函数
,
.
(1)讨论
在
上的单调性;
(2)当
时,讨论
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2aaf34611ec39ee81779c9fdaf33b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dcdd87d593df4a5c5e98d47fe1cfa6.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2663aa65026fd1c51f79262681271823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4910ca6f650498d99c61e1bed75c2783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a675abd1727f759b37e4054b81b1b71.png)
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2021-03-06更新
|
2426次组卷
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8卷引用:湖南省永州市2021届高三下学期二模数学试题
湖南省永州市2021届高三下学期二模数学试题(已下线)必刷卷02-2021年高考数学(理)考前信息必刷卷(新课标卷)(已下线)重组卷05-冲刺2021年高考数学之精选真题+模拟重组卷(新高考地区专用)山东省2021-2022学年高三10月“山东学情”联考数学试题C广东省深圳市高级中学(集团)2023届高三上学期期末数学试题(已下线)广东省深圳市高级中学(集团)2023届高三上学期期末数学试题变式题17-22湖南省邵阳市邵东市第三中学2024届高三上学期第二次月考数学试题河南省周口市恒大中学2024届高三上学期12月月考数学试题
7 . 已知抛物线
,焦点为F,过
外一点Q(不在x轴上),作
的两条切线,切点分别为A,B,直线QA,QB分别交y轴于C,D两点,记
的外心为M,
的外心为T.
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505227466358784/2507260326993920/STEM/0f056d8f20df4f808808bf8164e2baf9.png?resizew=180)
(1)若
,求线段CF的长度;
(2)当点Q在曲线
上运动时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1354240a807d0da2b51a19e055140165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e9b8a991d00fdd2810dda7adc54fd8.png)
![](https://img.xkw.com/dksih/QBM/2020/7/13/2505227466358784/2507260326993920/STEM/0f056d8f20df4f808808bf8164e2baf9.png?resizew=180)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d609cb7f8b4d79e8b65c0b8a0672d240.png)
(2)当点Q在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/849d513ba68f8904db5f0ed07c7ea208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882d6277e7f4e9c7b32c4f3fb5933290.png)
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解题方法
8 . 已知函数
.
(1)求
的单调区间;
(2)设
,
都有
成立,证明:
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e36e6158c7da6ebbf95da58658a998.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdf5828da3d88a6480c9ba954f9a649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33d41d398944a02f613784ff1ceeaf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9899b04fe82109e382fac168295a65db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33d41d398944a02f613784ff1ceeaf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/339db9d7fb9ff3f07172653144d4ba7a.png)
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9 . 已知定义在
上的函数
,其中
,e为自然对数的底数.
(1)求证:
有且只有一个极小值点;
(2)若不等式
在
上恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64cada0415883ac3c3df4d4afcbbde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2606dce43e1852cf7d43442d8a42b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
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名校
10 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fccbc9073b0dd0f56eb3f2d2754fa096.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef17fdbde17d43606fa029c1149387e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-06-24更新
|
1484次组卷
|
7卷引用:湖南省永州市六县2020届高三下学期6月第二次联考数学(理)试题