2012·黑龙江·三模
1 . f(x)=lnx,g(x)=f(x)+f′(x).
(Ⅰ)求g(x)的单调区间和最小值;
(Ⅱ)讨论g(x)与
的大小关系;
(Ⅲ)求a的取值范围,使得g(a)﹣g(x)<
对任意x>0成立.
(Ⅰ)求g(x)的单调区间和最小值;
(Ⅱ)讨论g(x)与
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571758980046848/1571758985773056/STEM/08529206e94b4003bb50354b34197dae.png)
(Ⅲ)求a的取值范围,使得g(a)﹣g(x)<
![](https://img.xkw.com/dksih/QBM/2014/6/5/1571758980046848/1571758985773056/STEM/9e59e1905c7647d194ec31b7792834a7.png)
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10卷引用:山东省烟台市2016-2017学年高二下学期期中学段考试数学(文)试题
山东省烟台市2016-2017学年高二下学期期中学段考试数学(文)试题【全国百强校】山东省济南第一中学2017-2018学年高二下学期期中考试数学(文)试题(已下线)2012届黑龙江省哈六中高三第三次模拟考试文科数学试卷(已下线)2011—2012学年江西省会昌中学高二下学期第二次月考文科数学试卷2011年普通高等学校招生全国统一考试文科数学(陕西卷)(已下线)2015届宁夏银川一中高三上学期第二次月考试卷文科数学试卷2017届河南息县第一高级中学高三文上段测五数学试卷天津市耀华中学2018届高三上学期第一次月考数学(文)试题12019届黑龙江省哈尔滨市第六中学高三第四次模拟数学(文)试题海南热带海洋学院附属中学2021届高三11月第二次月考数学试题
真题
名校
2 . 在平面直角坐标系xOy中,已知椭圆
.如图所示,斜率为k(k>0)且不过原点的直线l交椭圆C于A,B两点,线段AB的中点为E,射线OE交椭圆C于点G,交直线x=﹣3于点D(﹣3,m).
(1)求m2+k2的最小值;
(2)若|OG|2=|OD|∙|OE|,
(i)求证:直线l过定点;
(ii)试问点B,G能否关于x轴对称?若能,求出此时△ABG的外接圆方程;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4d3fac09fb943b5da320395ff0879a.png)
(1)求m2+k2的最小值;
(2)若|OG|2=|OD|∙|OE|,
(i)求证:直线l过定点;
(ii)试问点B,G能否关于x轴对称?若能,求出此时△ABG的外接圆方程;若不能,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/489c2274-66e7-4655-aeeb-9a6b7820e184.png?resizew=218)
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2016-12-03更新
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3332次组卷
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4卷引用:2011年普通高等学校招生全国统一考试文科数学(山东卷)
2011年普通高等学校招生全国统一考试文科数学(山东卷)天津市静海县第一中学2017-2018学年高二上学期期末终结性检测数学(理)试题(附加题)(已下线)专题45 盘点圆锥曲线中的定点问题——备战2022年高考数学二轮复习常考点专题突破(已下线)第五篇 向量与几何 专题5 调和点列 微点3 调和点列(三)
2011·江西·三模
3 . 已知椭圆
的离心率为
,以原点为圆心,椭圆的短半轴长为半径的圆与直线
相切.
(1)求椭圆
的方程;
(2)若过点
的直线与椭圆
相交于两点
,设
为椭圆上一点,且满足
(
为坐标原点),当
时,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447cf8fad38594b2c8863e20168e1ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc493a0ad349b89d41f9be3ae357d82.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de99c9c20ad2883a905320eaf5bf0179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd6c84e127366a8840b6720a9dacd8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb32ef8c72acd3c7b144af485c39835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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12卷引用:2012届山东省冠县武训高中高考模拟预测数学文试卷
(已下线)2012届山东省冠县武训高中高考模拟预测数学文试卷(已下线)2011届江西省师大附中高三第三次模拟理科数学试题(已下线)2011-2012学年河北省正定中学高二第一学期期末考试理科数学试卷(已下线)2011-2012学年辽宁省瓦房店市高级中学高二上学期期末理科数学试卷(已下线)2011-2012学年辽宁省瓦房店市高级中学高二上学期期末考试文科数学(已下线)2012届山西省四校高三第三次联考考试理科数学试卷(已下线)2012届黑龙江省哈六中高三第三次模拟考试理科数学试卷(已下线)2014届辽宁省抚顺市六校联合体高三上学期期中考试理科数学试卷(已下线)2014年吉林省延边州高考复习质量检测理科数学试卷(已下线)2013-2014学年新疆兵团农二师华山中学高二下学期期中理科数学试卷(已下线)2013-2014学年河北省正定中学高二上学期期末数学试卷河北省石家庄市正定中学2023-2024学年高二上学期期末数学试题
2014·山东日照·一模
名校
4 . 已知函数
,
.
(
)设曲线
在
处的切线为
,到点
的距离为
,求
的值.
(
)若对于任意实数
,
恒成立,试确定
的取值范围.
(
)当
时,是否存在实数
,使曲线
在点
处的切线与
轴垂直?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb0efa793fc95d2bbcc8eec1d375343f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c087511da0077205f79e5eda783263.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90bae886c8ab958aa4c693bf8e0627d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8b412b7053aea276c8e8dd3465af62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b26c238a3028a6403b56726435cac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
13-14高二下·河北邢台·阶段练习
名校
5 . 已知椭圆
:
的离心率为
,过椭圆
右焦点
的直线
与椭圆
交于点
(点
在第一象限).
(Ⅰ)求椭圆
的方程;
(Ⅱ)已知
为椭圆
的左顶点,平行于
的直线
与椭圆相交于
两点.判断直线
是否关于直线
对称,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/2015/4/29/1572087674814464/1572087680983040/STEM/5be4cb85ac80483e96c5eacf9478743f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3c755300698950d4d82946a4ef08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(Ⅱ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afce615c6b9049a6e43a7e18a5c014dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-02更新
|
2241次组卷
|
6卷引用:2014-2015学年山东青岛平度市三校高二上学期期末考试文科数学试卷
名校
6 . 已知函数
,
.
(1)求
的极值点;
(2)对任意的
,记
在
上的最小值为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecad04869b43c89cf22bcc80a92853e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26c3f8c63393f41b6365d975b6c269d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)对任意的
![](https://img.xkw.com/dksih/QBM/2014/2/24/1571522867879936/1571522873868288/STEM/a9227b3860d241cd9fffe2f2e377013d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a426b2b1114551cee091f38d0c25f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/019681dfa9daeafe43d667707c124233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450d33acdc40e74927ba3c476c7e30c9.png)
您最近一年使用:0次
14-15高三上·山东德州·期末
7 . 已知函数
.
(I)讨论
的单调性;
(Ⅱ)若
在(1,+
)恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff2edf906d293ba25face8b35221304.png)
(I)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4592d3d2120bba099e62fa68dec3d5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a27e72b96bc7af66c7472a9d7370e5b.png)
您最近一年使用:0次
13-14高一上·江苏盐城·期中
8 . 对于函数
,若存在实数对
,使得等式
对定义域中的每一个
都成立,则称函数
是“
型函数”.
(1) 判断函数
是否为“
型函数”,并说明理由;
(2) 若函数
是“
型函数”,求出满足条件的一组实数对
;
(3)已知函数
是“
型函数”,对应的实数对
为(1,4).当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6d27b23b1c41834d7516122f73f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e34c5eb4ca05084c4c6f55565fb7ec.png)
,若当
时,都有
,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fe86817946f4142d484bd67ce5f0c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(1) 判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b43539708e9663f5aa0b9336076936e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(2) 若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf44ef8807abfa79ffe1fb2919e9309e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681d6d27b23b1c41834d7516122f73f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e34c5eb4ca05084c4c6f55565fb7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcaceadc00d891e292c8bdff9e4ce64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbb01a7f5e9861aa185c6c63fcd58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b6ee958612051792de2e49fff0abf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
12-13高三上·山东枣庄·期末
解题方法
9 . 已知椭圆
的离心率为
,且椭圆上一点到两个焦点的距离之和为
.斜率为
的直线
过椭圆的上焦点且与椭圆相交于
两点,线段
的垂直平分线与
轴相交于点
.
(1)求椭圆的标准方程;
(2)求
的取值范围.
(3)试用
表示
的面积
,并求面积
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bcb166b53a49e393871bcb14a528792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56dba6ef0c00b3442464e6d0f39cf5c1.png)
(1)求椭圆的标准方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.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
11-12高三上·山东济南·阶段练习
解题方法
10 . 已知函数
.
(Ⅰ)当
时,求
在区间
上的最大值和最小值;
(Ⅱ)如果函数
在公共定义域D上,满足
,
那么就称
为的“伴随函数”.已知函数
,
.若在区间
上,
函数
是
的“伴随函数”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6bde5ecbf6966a15c0e6e3b15cd127.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b4e7aafb01b2104404fc9f0e5205c2.png)
(Ⅱ)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8361ee104bd1177d6262e1542cac95c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc40a37a51ff1dbff3bf0ff2e0adf7cf.png)
那么就称
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8361ee104bd1177d6262e1542cac95c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6f9c61ff17e2650ab7b7fb98e1619d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed96d837b14e2dc3425dbd84645ae74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2747dd40e29f1e55ad2c611e70a26130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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