2010·北京·二模
解题方法
1 . 已知椭圆
和圆
:
,过椭圆上一点P引圆O的两条切线,切点分别为A,B.
![](https://img.xkw.com/dksih/QBM/2013/6/28/1571259842387968/1571259847589888/STEM/a69117e79c5548af95ff12f69faa99e1.png?resizew=328)
(1)(ⅰ)若圆O过椭圆的两个焦点,求椭圆的离心率e的值;
(ⅱ)若椭圆上存在点P,使得
,求椭圆离心率e的取值范围;
(2)设直线AB与x轴、y轴分别交于点M,N,问当点P在椭圆上运动时,
是否为定值?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4ab88bc995ac5fc57518930a03c534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
![](https://img.xkw.com/dksih/QBM/2013/6/28/1571259842387968/1571259847589888/STEM/a69117e79c5548af95ff12f69faa99e1.png?resizew=328)
(1)(ⅰ)若圆O过椭圆的两个焦点,求椭圆的离心率e的值;
(ⅱ)若椭圆上存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df9b574c6b6a4c878bf425d4fa31d66.png)
(2)设直线AB与x轴、y轴分别交于点M,N,问当点P在椭圆上运动时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad3e95a9b0223e280a9034a91b29fbc.png)
您最近一年使用:0次
2011·北京西城·一模
2 . 已知抛物线
的焦点为
,过
的直线交
轴正半轴于点
,交抛物线于
两点,其中点
在第一象限.
(Ⅰ)求证:以线段
为直径的圆与
轴相切;
(Ⅱ)若
,
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b3932717847eb0859019f07a7445ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(Ⅰ)求证:以线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93dd4d854fbc236bccbd97a5d715fe97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1266096a1e8b8de08172b4ebc9d19659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3018c41828a4dae13bc106a973f61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23afe274ce13cdca597f9e1144181c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f31e2188a6843eea5270500ec4bd1fa.png)
您最近一年使用:0次
2011·北京西城·一模
名校
3 . 已知数列
的各项均为正整数,对于
,有
当
时,
______;
若存在
,当
且
为奇数时,
恒为常数
,则
的值为______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d737c1047a14cee12a6671383e244fa5.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572241494597632/1572241500454912/STEM/2579f4db845f466bb66ef520104dd030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d75f2ad81e3505ec16a2a3ccc1e5d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17f3bfd1e8c6d6284efdb69bcbada97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acca5aa6b2285d897a65c289c1b54ba.png)
若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad596ace5f1ae527c8f9fa8d3bedd9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412b61b3ea2f684925b14e78efae8a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
2016-11-30更新
|
1294次组卷
|
5卷引用:2011届北京市西城区高三一模试卷数学(理科)
(已下线)2011届北京市西城区高三一模试卷数学(理科)(已下线)2013届中国人民大学附属中学高考冲刺六理科数学试卷2016届上海市崇明区高考模拟数学试题山东省济南市莱芜第一中学2020-2021学年高三上学期11月月考数学试题北京名校2023届高三二轮复习 专题三 集合与数列 第3讲 集合与数列创新题
2011·北京海淀·二模
4 . 已知函数
.
.
(I)当
时,求曲线
在
处的切线方程(
);
(II)求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bde77fd5b0b0177b3e57cb31d4dac71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1a5f2533b8ea54b7022383f875666.png)
(I)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/606e5694c2f33033cced4e29d3152c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc0300ef61a9922c0f4f91123e6202.png)
(II)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2016-11-30更新
|
1046次组卷
|
5卷引用:2011届北京市海淀区高三第二学期第二次模拟(理科)数学题
(已下线)2011届北京市海淀区高三第二学期第二次模拟(理科)数学题(已下线)2013届中国人民大学附属中学高考冲刺十理科数学试卷(已下线)2010-2011学年河北省唐山一中高二下学期期末考试数学(文)新疆维吾尔自治区乌鲁木齐市第四十中学2024届高三上学期11月月考数学试题新疆维吾尔自治区伊宁市第三中学2024届高三下学期3月月考数学试题
5 . 若
为集合
且
的子集,且满足两个条件:
①
;
②对任意的
,至少存在一个
,使
或
.
则称集合组
具有性质
.
如图,作
行
列数表,定义数表中的第
行第
列的数为
.
(Ⅰ)当
时,判断下列两个集合组是否具有性质
,如果是请画出所对应的表格,如果不是请说明理由;
集合组1:
;
集合组2:
.
(Ⅱ)当
时,若集合组
具有性质
,请先画出所对应的
行3列的一个数表,再依此表格分别写出集合
;
(Ⅲ)当
时,集合组
是具有性质
且所含集合个数最小的集合组,求
的值及
的最小值.(其中
表示集合
所含元素的个数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e57fcd5fb8f222b56f449662144b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d6469b12a3e4abd19b42d9b07b14c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8e3c9f6f00803d033d60ecc03be61a.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50fb515ccb4e5ead5c9328e633c703cc.png)
②对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e689651e8d8f5438bf5afb6e72ee1c69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907c2308a58ddfd134ce4ca32b4a0cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d361f45fc89aa6f8342fe01265f2f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4232c44f99c25d566bca0a09d486cdba.png)
则称集合组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e57fcd5fb8f222b56f449662144b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
如图,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.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/fd45164ecad44e97205eccf6473b205f.png)
![]() | ![]() | … | ![]() |
![]() | ![]() | … | ![]() |
… | … | … | … |
![]() | ![]() | … | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
集合组1:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2419512d33074cdadd38811260f693.png)
集合组2:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76cc23f1a1dc847c21068e5378d2c4b.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764eff906937f9b1fb58e5abfb2eb8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f176b1357961977f6305e96b1d0ca0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b13b4469180a779ebbe6fc021c1fd98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f031d1d6bbb6d25d8ad933b016b969ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9ca68ba83be22ec5cbd6eba191cbc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
您最近一年使用:0次
2011·北京西城·二模
6 . 数列
满足
,
,其中
,
.
①当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd5367f5c88db960f534311d3476ef5.png)
_____ ;
②若存在正整数
,当
时总有
,则
的取值范围是_____ .
![](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/5357ce1e9d95681b072472cdd9d6f16d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b8e5990ef4ef314941a3154457a9d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac2c67be0e344a21e582980c0431c24.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558e11d700481dc414d5d073b4b88a3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcd5367f5c88db960f534311d3476ef5.png)
②若存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eae51f0310b87cde2e206643e9d25a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6a46c5fb744758ad83902819b83bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
7 . 某地实行阶梯电价,以日历年(每年1月1日至12月31日)为周期执行居民阶梯电价,即:一户居民用户全年不超过2880度(1度=千瓦时)的电量,执行第一档电价标准,每度电0.4883元;全年超过2880度至4800度之间的电量,执行第二档电价标准,每度电0.5383元;全年超过4800度以上的电量,执行第三档电价标准,每度电0.7883元.下面是关于阶梯电价的图形表示,其中正确的有
![](https://img.xkw.com/dksih/QBM/2016/3/4/1572518713155584/1572518718750720/STEM/f655ed09d6ab4a29808d0f14f841b84f.png)
参考数据:0.4883元/度
2880度=1406.30元,
0.5383元/度
(4800-2880)度+1406.30元=2439.84元.
![](https://img.xkw.com/dksih/QBM/2016/3/4/1572518713155584/1572518718750720/STEM/f655ed09d6ab4a29808d0f14f841b84f.png)
参考数据:0.4883元/度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04490c62035e93ac5446d2d017facc41.png)
0.5383元/度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04490c62035e93ac5446d2d017facc41.png)
A.①② | B.②③ | C.①③ | D.①②③ |
您最近一年使用:0次
2016-03-04更新
|
511次组卷
|
4卷引用:2016届北京市丰台区高三上学期期末联考文科数学试卷
2016届北京市丰台区高三上学期期末联考文科数学试卷2016届宁夏·海南高三三轮冲刺猜三文科数学试卷2016届高三(亮剑·快乐考生)三轮冲刺猜题(三)文数试卷(已下线)《2018-2019学年同步单元双基双测AB卷》必修一 专题八 函数模型与应用 A卷
2012·北京·一模
8 . 已知椭圆
的上顶点为
,两个焦点为
、
,
为正三角形且周长为6.
(1)求椭圆
的标准方程;
(2)已知圆
,若直线
与椭圆
只有一个公共点
,且直线
与圆
相切于点
;求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd432589cb00c29cac1806288e99ed0.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac35b1e8a952aac4f4cdaaf02d868d04.png)
您最近一年使用:0次
2010·北京石景山·一模
9 . 已知函数
,在点
处的切线方程为
.
(I)求函数
的解析式;
(II)若对于区间
上任意两个自变量的值
,都有
,求实数
的最小值;
(III)若过点
,可作曲线
的三条切线,求实数
的取值范围.
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/f5259d3bc6004ff290a02bb953f408b2.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/88e53859d9b04560a2e570309de9fdf2.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/6ec791d412e84be6a1aeb24b043ec0a1.png)
(I)求函数
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/59ba723dae9e449488ece8de44d19ad4.png)
(II)若对于区间
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/8778eaf09b8b496a8d6aa9b425ca55cc.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/257f8c0407de4db9a438b5d9f1042c3a.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/12ba0c1edb804e8b9d220060fa0ed7a2.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/7c03731a8f154cff87116c41ad6af005.png)
(III)若过点
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/ed8874c966174811bf45dfb2d8fa9968.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/35a415d8fbdf407fa1915bd0c6266850.png)
![](https://img.xkw.com/dksih/QBM/2014/9/17/1571857020592128/1571857026285568/STEM/3c309915972648f9812943656f40f5b5.png)
您最近一年使用:0次
2010·北京石景山·一模
名校
10 . 已知函数
.
(Ⅰ)若
,求曲线
在点
处的切线方程;
(Ⅱ)若函数
在其定义域内为增函数,求正实数p的取值范围;
(Ⅲ)设函数
(
为自然对数底数),若在
上至少存在一点
,使得
成立,求实数p的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea25bf65d4e08ef94224efe45b16844a.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(Ⅱ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅲ)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6357128f4acb43012e75092454d3f633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/579e2c39e6c0a640357e3b0ccd6f954a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae17887ccf795c630b89ff5c9f72813a.png)
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2016-12-03更新
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18卷引用:北京市石景山区2010届高三一模考试(数学理)
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