1 . 已知函数
.
(1)这比较
与
的大小;
(2)求证:当
时,
.参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3d74bc831a959f5d2a2b016548eba0.png)
(1)这比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0dc5e52dffcf333d8fb6b4fbb88351d.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98311b195ab694abe941ab9b3f2afbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e392fde3c13f59a80a19a277995a145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d3c5808ad653e9c0af246789f0b221.png)
您最近一年使用:0次
2022-11-24更新
|
238次组卷
|
2卷引用:山东省青岛市莱西市2022-2023学年高三上学期期中数学试题
2 . 已知函数
是函数
的导函数.
(1)求函数
的单调区问;
(2)设
,试比较
与
的大小,并说明理由;
(3)若数列
的通项
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d9dc938120de768c9985a10b13efc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b95b84c315af9ba942872ba2c1ed02.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d100c22435a23e017cfe6f535379d3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c81acd74ca60afd8764de4865aeadf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392009df043af5de7260a7608c8181c6.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c2a93f134ec21d101bc0b5b856af57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f036ff1e67682117d6f1c40075c8a701.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)若
,证明:
;
(2)若
,
对任意正实数x恒成立,求正实数b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4077cd00daaeb5df82b1b202d40e670.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2584d4e78881413d8ddd1ec84011db2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5eec90c8155bc621f83d6728ad73e7.png)
您最近一年使用:0次
2022-11-15更新
|
408次组卷
|
4卷引用:山东省青岛市西海岸新区2022-2023学年高三上学期期中考试数学试题
解题方法
4 . 如图,已知椭圆
的左、右顶点为
、
,又
、
与椭圆短轴的一个端点组成的三角形面积为
.圆
的圆心为椭圆的左顶点
.
(1)求椭圆
的方程;
(2)当圆
半径
时,过椭圆外一点垂直于
轴的圆
的切线为
,点
是椭圆
上位于
轴上方的动点,直线
、
与直线
分别交于
、
两点,求
的最小值;
(3)圆A与椭圆
交于点
、
.点
是椭圆
上异于
、
的任意一点,且直线
、
分别与
轴交于点
、
,
为坐标原点.求证:
为定值.
![](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/7f9e8449aad35c5d840a3395ea86df6d.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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5f65e93fbccf9d7743ea844f2ad57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/3/7607ec66-8833-4927-be03-9ed992a2f631.png?resizew=260)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6ee74e19ae838c6ac060ba16569e25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803a617fb53e67edbc2955cb629c329b.png)
(3)圆A与椭圆
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2382c2608298c372d89106b359c0f495.png)
您最近一年使用:0次
解题方法
5 . 已知双曲线
:
的离心率为
,且焦点到渐近线的距离为1.
(1)求双曲线
的方程;
(2)若动直线
与双曲线
恰有1个公共点,且与双曲线
的两条渐近线分别交于
,
两点,
为坐标原点,证明:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若动直线
![](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/c5db41a1f31d6baee7c69990811edb9f.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
您最近一年使用:0次
2022-11-09更新
|
685次组卷
|
4卷引用:山东省多校2022-2023学年高二上学期期中联合调考数学试题
6 . 已知函数
和
有相同的最大值.
(1)求
,并说明函数
在(1,e)上有且仅有一个零点;
(2)证明:存在直线
,其与两条曲线
和
共有三个不同的交点,并且从左到右的三个交点的横坐标成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b26f55c7c29644dfe0277d3e2adf10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ecfbb8b013b3dc3a8f27f60d692991.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
(2)证明:存在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
:
的左、右焦点分别为
,
,长轴长为4,A,B是
上关于原点对称的两个动点,当
垂直于x轴时,
的周长为
.
(1)求
的方程;
(2)已知
的离心率
,直线
与
交于点M(异于点A),直线
与
交于点N(异于点B),证明:直线MN过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e19960ba707a6b1d55460c6a5855dd3.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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce448aff0208b52d0e8688ac590d221.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8433146cfb355bc3c49d35cb488868b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
您最近一年使用:0次
2022-12-07更新
|
850次组卷
|
5卷引用:山东省临沂市沂水县2022-2023学年高二上学期期中考试数学试题
山东省临沂市沂水县2022-2023学年高二上学期期中考试数学试题海南省海南中学2023-2024学年高二上学期期中考试数学试题(已下线)期中真题必刷椭圆60题(4个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)安徽省定远中学2023届高三下学期第二次模拟数学试卷宁夏银川市第二中学2023-2024学年高三下学期适应性考试数学(理科)试题
名校
8 . 已知函数
.
(1)讨论函数
的单调性;
(2)设函数
有两个极值点
,
.
(i)求实数a的取值范围;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03431588b58c61c29bc4714074fb470d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5274e3d6eb5da84ca3b95a500617728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
(i)求实数a的取值范围;
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747fdf10ab847b944354b317bc4adb3a.png)
您最近一年使用:0次
2022-11-04更新
|
833次组卷
|
4卷引用:山东省烟台市2022-2023学年高三上学期期中数学试题
9 . 已知轨迹
上任一点
与定点
的距离和
到定直线
的距离的比为
.
(1)求轨迹
的方程,并说明轨迹表示什么图形?
(2)设点
,过点
且斜率为
的动直线
与轨迹
交于
两点,直线
分别交圆
于异于点
的点
,设直线
的斜率为
,直线
的斜率分别为
.
①求证:
为定值;
②问:直线
是否过一定点,若过,请求出定点;若不过,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55307ac4f2f3cd3b60bdf21c533290e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d314b47d37c9f58e05ad11f3e68e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b730ecafb4233ae861b235d24ab40ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdd4e2521541c5a5a8ea831545f1030c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dde9d5e2426cc9da23014b91f03f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e265ce107592c375b78007107a9c00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dde9d5e2426cc9da23014b91f03f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2d18088eecb661fd38b53f6fd0b09a.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ee950caafdafed20520afb0ce328d1.png)
②问:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.
(1)若
恒成立,求
的取值范围;
(2)证明:对任意
;
(3)讨论函数
零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4408d41d16260ea1c6c5db1af1270b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40552d8e956b30086ac9a35614d776a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3498e9e59c2230e54b4c802916a14e76.png)
(3)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2022-11-22更新
|
644次组卷
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6卷引用:山东省滨州市邹平市第一中学2022-2023学年高三上学期期中考试数学试题
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