1 . (1)已知a、b、c是不全相等的正数,且
.求证:
.
(2)用反证法证明:若函数
在区间
上是增函数,则方程
在区间
上至多只有一个实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa54caec3efb5765d189b06789c336ad.png)
(2)用反证法证明:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
您最近一年使用:0次
名校
2 . 若
时,函数
取得极大值或极小值,则称
为函数
的极值点.已知函数
,其中
为正实数.
(1)若函数
有极值点,求
的取值范围;
(2)当
和
的几何平均数为
,算术平均数为
.
①判断
与
和
的几何平均数和算术平均数的大小关系,并加以证明;
②当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c18b8de6c7eb43276a04f94c3c86e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eee411aceac3fe67a2baae3bfb17f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be423b2718619420c6545d02b6070a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f0f24d3528e467f3978cd4422433e2.png)
①判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fce088a946b9934e891fb4ca0657a0df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
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2024-03-03更新
|
882次组卷
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5卷引用:甘肃省天水市第一中学2023-2024学年高二下学期4月学段检测数学试题
3 . 已知
为椭圆
的右焦点,离心率为
.
(1)求
的方程;
(2)若
是平面上的动点,直线
不与坐标轴垂直,从下面两个条件中选择一个,证明:直线
经过定点.
①
为椭圆
上两个动点,且
;
②
为椭圆
上两个动点,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b406c5e06b7790b2e481a8ce3f5e33c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3551efb72b95def8f1877b5c38d71192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a877428408d09ac0112f833e54a8e34a.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282298a866831ea4a8cdf96ae28c0aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a877428408d09ac0112f833e54a8e34a.png)
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4 . 已知点
,圆
,点
是圆
上的任意一点.动圆
过点
,且与
相切,点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若与
轴不垂直的直线
与曲线
交于
、
两点,点
为
与
轴的交点,且
,若在
轴上存在异于点
的一点
,使得
为定值,求点
的坐标;
(3)过点
的直线与曲线
交于
、
两点,且曲线
在
、
两点处的切线交于点
,证明:
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893f6f9256d7e91289d294479ec75c13.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba53065eb180a682305fddb95d14b62f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)若与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c4016c26d5178f242c01b881eb66950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ddcd912a431f2c6092ae492b7a0482.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbcd0aebdd8bd688d108834747009f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-12-21更新
|
277次组卷
|
4卷引用:甘肃省白银市靖远县第四中学2023-2024学年高二下学期开学考试数学试题
甘肃省白银市靖远县第四中学2023-2024学年高二下学期开学考试数学试题山东省潍坊市2023-2024学年高二上学期普通高中学科素养能力测评数学试题广东省惠州市第一中学2024届高三元月阶段测试数学试题(已下线)专题4 抛物线切线与阿基米德三角形【练】(压轴题大全)
5 . 帕德近似是法国数学家亨利·帕德发明的用有理多项式近似特定函数的方法.给定两个正整数
,
,函数
在
处的
阶帕德近似定义为:
,且满足:
,
,
,
.已知
在
处的
阶帕德近似为
.注:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57986f853e0bfec0e2128309e7d71dad.png)
(1)求实数
,
的值;
(2)求证:
;
(3)求不等式
的解集,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab984fa2801f780e08903b339c9d041f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d8ef6c18c8edf9f4c781376d5ce400a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa6b902edcff913a34589487e17c9fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf17fbb5f74fa34593ac47a0e8d3269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089b65749e52fc6346eab9bb5c49e5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e96546b3259afe4add331673fb835c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d307aa65d930bc8e51835eb147de513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d128f7851b7771f95bffbdbf3ced02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57986f853e0bfec0e2128309e7d71dad.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f30a295015a8b1b038076f55f6ec928.png)
(3)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ccd45ddc39488a73ebb0025e517059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
您最近一年使用:0次
2023-04-26更新
|
2497次组卷
|
17卷引用:甘肃省白银市靖远县第四中学2023-2024学年高二下学期4月月考数学试题
甘肃省白银市靖远县第四中学2023-2024学年高二下学期4月月考数学试题山东省济南市2022-2023学年高二下学期期中数学试题(已下线)专题2 导数在研究函数单调性中的应用(B)重庆市璧山来凤中学校2023-2024学年高二下学期3月月考数学试题广东省中山市华辰实验中学2023-2024学年高二下学期第一次月考数学试题(已下线)模块四 期中重组篇(高二下山东) 重庆市巴蜀中学校2023届高三下学期4月月考数学试题吉林省白山市抚松县第一中学2022-2023学年高三第十一次校内模拟数学试题(已下线)重难点突破02 函数的综合应用(九大题型)(已下线)第十章 导数与数学文化 微点2 导数与数学文化(二)(已下线)第六套 九省联考全真模拟(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编(已下线)微考点8-1 新高考新题型19题新定义题型精选(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)(已下线)模块3 第8套 复盘卷(已下线)模块一 专题2 《导数在研究函数单调性中的应用》 B提升卷(苏教版)(已下线)专题12 帕德逼近与不等式证明【练】
6 . 在①C的渐近线方程为
②C的离心率为
这两个条件中任选一个,填在题中的横线上,并解答.
已知双曲线C的对称中心在坐标原点,对称轴为坐标轴,点
在C上,且______.
(1)求C的标准方程;
(2)已知C的右焦点为F,直线PF与C交于另一点Q,不与直线PF重合且过F的动直线l与C交于M,N两点,直线PM和QN交于点A,证明:A在定直线上.
注:如果选择两个条件分别解答,则按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
已知双曲线C的对称中心在坐标原点,对称轴为坐标轴,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13428e6305dfc0ca9883044f525b6b5a.png)
(1)求C的标准方程;
(2)已知C的右焦点为F,直线PF与C交于另一点Q,不与直线PF重合且过F的动直线l与C交于M,N两点,直线PM和QN交于点A,证明:A在定直线上.
注:如果选择两个条件分别解答,则按第一个解答计分.
您最近一年使用:0次
2023-01-14更新
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774次组卷
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5卷引用:甘肃省庆阳市2022-2023学年高二上学期期末考试数学试题
甘肃省庆阳市2022-2023学年高二上学期期末考试数学试题辽宁省辽阳市协作校2022-2023学年高二上学期期末考试数学试题(已下线)第04讲 3.2.2双曲线的简单几何性质(2)山东省烟台市龙口第一中学等校2023-2024学年高二上学期12月月考数学试题(已下线)2023年新课标全国Ⅱ卷数学真题变式题19-22
7 . 已知
.在以下A,B,C三问中任选两问作答,若三问都分别作答,则按前两问作答计分,作答时,请在答题卷上标明所选两问的题号.
(A)求
;
(B)求
;
(C)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e202e9da891cf578042d485191f6302.png)
(A)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65fc200f10b97588a0c9896277c9c64.png)
(B)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7da9fbd8b19f8d234eef4738f31d5f.png)
(C)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f2348d412bd417463e36370e51748e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec9fc98496fc7aafd2c0287f41b803e8.png)
您最近一年使用:0次
名校
8 . 求证:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee48dbb902af988191681469b37ce54f.png)
(2)对于任意角
,
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee48dbb902af988191681469b37ce54f.png)
(2)对于任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be3552729409fce16518fdc01c7b5b4.png)
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名校
9 . 已知实数p满足不等式
,用反证法证明:关于x的方程
无实数根.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63677dc1c787631f6d59899c20e4a218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460717532e94a6abe9ea0e7c74bf87fb.png)
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