名校
解题方法
1 . 已知函数
.
(1)若
恰有两个极值点,求实数
的取值范围;
(2)若
的两个极值点分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/125c0225ea4ef140fd3236739a9aa024.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ced2ceab6d52a14af4d477a9ff09823.png)
您最近一年使用:0次
2024-04-01更新
|
513次组卷
|
4卷引用:甘肃省武威市天祝第一中学、民勤县第一中学2023-2024学年高二下学期第一次月考数学试题
甘肃省武威市天祝第一中学、民勤县第一中学2023-2024学年高二下学期第一次月考数学试题吉林省珲春市第一高级中学、图们市第二高级中学2023-2024学年高二上学期期末考试数学试题(已下线)专题07 函数的极值和最值的应用8种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)青海省海东市第一中学2023-2024学年高二下学期第一次月考数学试题
名校
解题方法
2 . 已知双曲线
与双曲线
的渐近线相同,且M 经过点 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace9fcc08faacf15593012ec13916374.png)
的焦距为4.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/f427b0cb-5844-4b12-9df7-2a90b8cd59ce.png?resizew=164)
(1)求M 和
的方程;
(2)如图,过点 T(0,1)的直线 l(斜率大于0)与双曲线 M 和 N 的左、右两支依次相交于A,B,C,D,若
求直线 l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31380cee127ebeb85e866d355fc1eca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c97cdfbccfac205f7b826a73d3579a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace9fcc08faacf15593012ec13916374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/f427b0cb-5844-4b12-9df7-2a90b8cd59ce.png?resizew=164)
(1)求M 和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)如图,过点 T(0,1)的直线 l(斜率大于0)与双曲线 M 和 N 的左、右两支依次相交于A,B,C,D,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643adde2c8f41e319097b20af7e2f578.png)
您最近一年使用:0次
2024-03-24更新
|
610次组卷
|
2卷引用:甘肃省陇南市部分学校2024届高三一模联考数学试题
解题方法
3 . 已知函数
.
(1)求函数
的极值点及极值;
(2)若
,且
,求证:
为自然对数的底
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b614cf5dd093d2dcad7e25bcaeb7cb4.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636a8d9e362e768e825a98afdea2bd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c35d9402d1cf63a34bc61b6602322032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
您最近一年使用:0次
4 . 已知椭圆
的右焦点为
,设直线
:
与
轴的交点为
,过点
且斜率为
的直线
与椭圆交于
、
两点,
为线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/0b5cb170-5991-46e2-9f57-b0691c4732cd.png?resizew=194)
(1)若
,求直线
的倾斜角;
(2)设直线
交直线
于点
.
①求直线
的斜率;
②求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/0b5cb170-5991-46e2-9f57-b0691c4732cd.png?resizew=194)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f76cc09dfa324e07f7bb5919eeaba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)设直线
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
①求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38f3fb2aa72365b99509f623c3f31aa.png)
您最近一年使用:0次
5 . “工艺折纸”是一种把纸张折成各种不同形状物品的艺术活动,在我国源远流长.某些折纸活动蕴含丰富的数学内容,例如:用一张圆形纸片,按如下步骤折纸(如图).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/90427c07-5298-4cbd-ba64-d5520a07d701.png?resizew=262)
步骤1:设圆心为E,在圆内异于圆心处取一点,标记为F;
步骤2:把纸片折叠,使圆周正好通过点F;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕.
已知这些折痕所围成的图形是一个椭圆.若取半径为6的圆形纸片,设定点F到圆心E的距离为4,按上述方法折纸.
(1)以点F、E所在的直线为x轴,建立适当的坐标系,求折痕围成的椭圆C的标准方程;
(2)若过点
且不与y轴垂直的直线l与椭圆C交于M,N两点,在x轴的正半轴上是否存在定点
,使得直线TM,TN的斜率之积为定值?若存在,求出该定点和定值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/90427c07-5298-4cbd-ba64-d5520a07d701.png?resizew=262)
步骤1:设圆心为E,在圆内异于圆心处取一点,标记为F;
步骤2:把纸片折叠,使圆周正好通过点F;
步骤3:把纸片展开,并留下一道折痕;
步骤4:不停重复步骤2和3,就能得到越来越多的折痕.
已知这些折痕所围成的图形是一个椭圆.若取半径为6的圆形纸片,设定点F到圆心E的距离为4,按上述方法折纸.
(1)以点F、E所在的直线为x轴,建立适当的坐标系,求折痕围成的椭圆C的标准方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104858bd2e55876487eade49e84d62c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb2818cd5000adaa66af6a2e09a6fcf.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆
的离心率为
,且过点
.
(1)求椭圆
的标准方程;
(2)若椭圆的上顶点为点
,过点
的直线交椭圆于点
,证明:
为定值,并求出定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82acb787a4030235fcec90e8320ca9c1.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若椭圆的上顶点为点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc57241e3b3057dfb0be2821381c8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37ada8d3b59c983880b013ad973ae55.png)
您最近一年使用:0次
7 . 英国数学家泰勒发现的泰勒公式有如下特殊形式:当
在
处的
阶导数都存在时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661a2ffa74a30c0b1c0a0ea0fdc8bb3c.png)
.注:
表示
的2阶导数,即为
的导数,
表示
的
阶导数,该公式也称麦克劳林公式.
(1)根据该公式估算
的值,精确到小数点后两位;
(2)由该公式可得:
.当
时,试比较
与
的大小,并给出证明;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f1d8cb672db61735be7cbcd3d50bf9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661a2ffa74a30c0b1c0a0ea0fdc8bb3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35993bd1db970330494665d925c0be7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)根据该公式估算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67aace59c071f37a444495678497ef0.png)
(2)由该公式可得:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba15a427babacf319deb9c4dd8d58b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ea093173f74807332e08bde42f25e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd9f874878e11c3fa25143023e8f95a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5cf9c12181dd8683944b2b30bf8e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa80dea5928f0be2b39075a434742686.png)
您最近一年使用:0次
2024-03-14更新
|
3384次组卷
|
13卷引用:甘肃省兰州市第五十八中学2024届高三第二次高考仿真考试数学试题
甘肃省兰州市第五十八中学2024届高三第二次高考仿真考试数学试题湖北省八市2024届高三下学期3月联考数学试卷江苏省连云港市东海高级中学2023-2024学年高二下学期强化班第一次月考数学试题(已下线)第10题 导数压轴大题归类(2)(高三二轮每日一题)河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷安徽省蚌埠市第二中学2023-2024学年高二下学期3月月巩固检测数学试题江苏省苏州市张家港市沙洲中学2023-2024学年高二下学期3月阶段性测试数学试题山西省晋城市第一中学校2023-2024学年高二下学期第二次调研考试数学试题广东省东莞市外国语学校2023-2024学年高二下学期第一次阶段性考试(4月)数学试题河南省许昌市禹州市高级中学2024届高三下学期4月月考数学试题吉林省长春市第二中学2023-2024学年高二下学期第一学程考试(4月)数学试题(已下线)压轴题05数列压轴题15题型汇总-1广东省深圳市2024届高三下学期三模数学试题
解题方法
8 . 如图,
为坐标原点,
为抛物线
的焦点,过
的直线交抛物线于
两点,直线
交抛物线的准线于点
,设抛物线在
点处的切线为
.
与
轴的交点为
,求证:
;
(2)过点
作
的垂线与直线
交于点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2e095298cfb23d9f47811556fc9f9a.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3eae6aa7672b9eef122fb7a1dab14e.png)
您最近一年使用:0次
2024-03-13更新
|
1607次组卷
|
5卷引用:甘肃省兰州市2024届高三下学期三模数学试题
甘肃省兰州市2024届高三下学期三模数学试题湖北省七市州2024届高三下学期3月联合统一调研测试数学试题山东省潍坊市昌乐北大公学学校2024届高三下学期3月监测数学试题四川省成都市教育科学研究院附属中学2023-2024学年高三下学期4月综合测试数学(理科)试题(已下线)湖北省七市州2024届高三下学期3月联合统一调研测试数学试题变式题16-19
名校
解题方法
9 . 已知双曲线
的两条渐近线互相垂直,且经过点
.
(1)求双曲线
的标准方程;
(2)若过点
的直线交双曲线同一支于两点
,设
中点为
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a919c4be4677648d9a5fc2d717283bb.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8547f2b4e89b0ae1445bda02d46f0668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
名校
解题方法
10 . 已知椭圆
的离心率为
,点
在
上,
的长轴长为
.
(1)求
的方程;
(2)已知原点为
,点
在
上,
的中点为
,过点
的直线与
交于点
,且线段
恰好被点
平分,判断
是否为定值?若为定值,求出该定值;若不为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d01bbdcc25ec5eedb21c14c82fa6ec6.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/8806602a7954aa6a067d8c6aed8e239f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知原点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834a37be1f8a4100c7bbc5972cca1e89.png)
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2024-03-07更新
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3卷引用:甘肃省部分学校2024届高三下学期2月开学考试数学试题