解题方法
1 . 已知
为双曲线
的左焦点,
是
的右顶点,点
在过点
且斜率为
的直线上,
且线段
的垂直平分线经过点
,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47cfe4e08c06bde245e58aa22485044c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee1ec65afc7021cc0479392e27d82bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知
和
,数列
和
的公共项由小到大组成数列
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4b5779873cb3f4366dbfdb983dec81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8becb97e55f0db7e62abbb86aff80b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ef8539a7a09303a95b4e79fb9949fc.png)
A.![]() |
B.![]() |
C.数列![]() ![]() ![]() |
D.数列![]() ![]() ![]() |
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3 . 定义:在一个有穷数列的每相邻两项之间插入这两项的和,形成新的数列,我们把这样的操作称为该数列的一次“和扩充”,例如:数列
经过第一次“和扩充”后得到数列
;第二次“和扩充”后得到数列
.设数列
经过
次“和扩充”后得到的数列的项数为
,所有项的和为
.
(1)若
,求
;
(2)求不等式
的解集;
(3)是否存在数列
,使得数列
为等比数列?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680e9ef551b325387ab31dca1f893705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa2d5ffc86bda25b7fd377267ae3e7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef1d5a07307b7d2603995105ab2490f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33d09c34e89bc99fbeb30bac80d4f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a642ed9870f81d906816bc0db3d621c.png)
(2)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dcd08431daac10be93e6fafbc5d4a90.png)
(3)是否存在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/863d3bc9596595b16499a46479526680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846fa57d92d6ad44d6a0cafad1e71ed4.png)
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解题方法
4 . 已知抛物线
的焦点为
,直线
交抛物线于
两点,
为抛物线
的准线与
轴的交点,直线
分别交抛物线于
两点(点
异于点
,
),
为坐标原点,则实数
的取值范围为__________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b21b94a2bb768ccbc65c33f9c4ed923.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c654f3bb56ece42d29a9f14cca37bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/3eb2d74932ede98011219d319f5b9995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b21b94a2bb768ccbc65c33f9c4ed923.png)
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5 . 已知函数
.
(1)如果
,求曲线
在
处的切线方程;
(2)如果对于任意的
都有
且
,求实数
满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94136a5fcb9f6d52342f1a572c3d5b54.png)
(1)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba0cdede7f0a093df20271a6d2ea53c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d02059613da3797ae406925b6ee5b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c3319647314c3b6d82958a909acd2a.png)
(2)如果对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4138f6987cd2ee9e56b2ac80e84f9e24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:2024届河南省名校联盟考前模拟大联考三模数学试题
6 . “奔驰定理”因其几何表示酷似奔驰的标志得来,是平面向量中一个非常优美的结论.奔驰定理与三角形四心(重心、内心、外心、垂心)有着神秘的关联.它的具体内容是:已知M是
内一点,
,
,
的面积分别为
,
,
,且
.以下命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d011d6ad89d0b033f96c2efbb314d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e8ecb371ce77dca5554e8e03b41386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4b0c4b339f44bbac0e275eb0718234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319b6a5373bc8eb13772b8e6d047779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea3c7cd2f23b4521e64a7e64844ec48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e8a7f6c535fc3cd270af428d55f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63a8338380587c4466483cc9b2fd2bb.png)
A.若![]() ![]() |
B.若M为![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若M为![]() ![]() ![]() |
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解题方法
7 . 已知
,且
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994d5f1faab6513a410af7f971795eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5859a48ed015c2c236fa3ba6f4b3cc62.png)
A.9 | B.12 | C.36 | D.48 |
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8 . 已知
分别满足下列关系:
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c034fe93ffb4be7bec50b0c129595a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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名校
9 . 曲线
与曲线
有公切线,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84178064b72d04058531dda176e52b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:广东省茂名市高州市2024届高三第一次模拟考试数学试题
广东省茂名市高州市2024届高三第一次模拟考试数学试题(已下线)专题7 两个函数公切线问题【讲】(高二期末压轴专项)山东省泰安市新泰市第一中学东校2023-2024学年高二下学期第二次质量检测数学试题山东省淄博实验中学2023-2024学年高二下学期第二次诊断考试(6月月考)数学试题
10 . 设函数
,直线
是曲线
在点
处的切线.
(1)当
时,求
的单调区间.
(2)求证:
不经过点
.
(3)当
时,设点
,
,
,
为
与
轴的交点,
与
分别表示
与
的面积.是否存在点
使得
成立?若存在,这样的点
有几个?
(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417cb4681ede2fc845d8214e48b41bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0a205f3a39c7dcad9411c5d801f9a9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32832923ae26bd414843e4ca870d1c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2c84e7b41a841a230ed5f8a42309aa.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abf9984cf7923373be05bbb2dfe41f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3998987160c168c3fc50cb2db66211f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c557708bf41b5fd4dbb8f04278e8a824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d166e13302046b25a2fa36af1e72f7a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f0f038ebe04ea9441bd5eedf069806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea05b8641371b1d221d9b4143ef3b37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e02569631057452e44347c1b8bcce37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e0d1953b7e72fac5593b4d7477b688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f07d589cd4bf0d4beb4c9f28bd2587.png)
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7卷引用:2024年北京高考数学真题
2024年北京高考数学真题专题03导数及其应用(已下线)2024年北京高考数学真题变式题16-21专题13导数及其应用(已下线)五年北京专题09导数及其应用(已下线)三年北京专题09导数及其应用(已下线)第01讲 导数的概念及其意义、导数的运算(十二大题型)(练习)-2