名校
解题方法
1 . 在平面直角坐标系中,确定若干个点,点的横、纵坐标均取自集合
,这样的点共有n个.
(1)求以这n个点中的2个点为端点的线段的条数;
(2)求这n个点能确定的直线的条数;
(3)若从这n个点中选出3个点分别为三角形的3个顶点,求这样的三角形的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109fea550364bb2aabef823b83ccb37c.png)
(1)求以这n个点中的2个点为端点的线段的条数;
(2)求这n个点能确定的直线的条数;
(3)若从这n个点中选出3个点分别为三角形的3个顶点,求这样的三角形的个数.
您最近一年使用:0次
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2 . 如图,在四棱锥
中,平面
平面
,
,底面
为等腰梯形,
,且
.
平面
;
(2)若点A到平面PBC的距离为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb05b8b630052ff544249ebd72d95d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852847ba02c2b62abf27e9cc11f596a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若点A到平面PBC的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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3 . 已知
(其中
为自然对数的底数).
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,判断
是否存在极值,并说明理由;
(3)若对任意实数
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04d21bd20b782e1b1a030b04d8394fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66367f83e841caba04d29fceaa5cf4f7.png)
(1)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/68c6b6a11760d0724b0b60e55970e229.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9baa33e282d8b0b45c68b268ac610044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024·全国·模拟预测
名校
4 . 甲、乙两人进行象棋比赛,赛前每人有3面小红旗.一局比赛后输者需给赢者一面小红旗;若是平局不需要给红旗,当其中一方无小红旗时,比赛结束,有6面小红旗者最终获胜.根据以往的两人比赛结果可知,在一局比赛中甲胜的概率为0.5,乙胜的概率为0.4.
(1)若第一局比赛后甲的红旗个数为X,求X的分布列和数学期望;
(2)若比赛一共进行五局,求第一局是乙胜的条件下,甲最终获胜的概率(结果保留两位有效数字);
(3)记甲获得红旗为
面时最终甲获胜的概率为
,
,
,证明:
为等比数列.
(1)若第一局比赛后甲的红旗个数为X,求X的分布列和数学期望;
(2)若比赛一共进行五局,求第一局是乙胜的条件下,甲最终获胜的概率(结果保留两位有效数字);
(3)记甲获得红旗为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7435d45cd9df9a16bc01188c8fdef1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94b1e988f6574093ecf0675049af801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0644cc6e89583bcb9564d85a80ee6c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b0e645eb76eaea9a16d406e85f2cad.png)
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解题方法
5 . 在函数极限的运算过程中,洛必达法则是解决未定式
型或
型极限的一种重要方法,其含义为:若函数
和
满足下列条件:
①
且
(或
,
);
②在点
的附近区域内两者都可导,且
;
③
(
可为实数,也可为
),则
.
(1)用洛必达法则求
;
(2)函数
(
,
),判断并说明
的零点个数;
(3)已知
,
,
,求
的解析式.
参考公式:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955689923ebe1be46168295644f4a178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef9c42b3bfeac3b11f6f2f7c5227967.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e7490f915131bdb436285e3fb284817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba30ad5f21a62879bba0aee45b81507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e530f639eaa27858ed7db451e2ed576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4658c5369aa8a25ea8580f524e87da.png)
②在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90c83ba8da83994264cb5b8b2f15f4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56af5e590e8152c9a7ded6209e446ced.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de3f06b6df7b949c5e6b406a661079f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f32baa7d29934cde8a5203388ed18c6.png)
(1)用洛必达法则求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782ec35f212cb1448863b4b15e806814.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161ab6e6a97905ea5bb2b3fc390ab7d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deda945164283569437cda6976fe35ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddd2a1b30b9ad891172f7f21c5a2701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc2b7be871fef904c94ef6360ee32bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f385eacc118fe9b5f0c23182929d6a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9005b464218c70a9963452693645cf2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9949db821a880972efbfb32354cd6bd.png)
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2024-04-24更新
|
785次组卷
|
5卷引用:2024届河北省邢台市部分高中二模数学试题
2024届河北省邢台市部分高中二模数学试题(已下线)模块4 二模重组卷 第3套 全真模拟卷(已下线)专题14 洛必达法则的应用【练】河南省郑州市宇华实验学校2024届高三下学期5月月考数学试题河北省衡水中学2023-2024学年高三下学期期中自我提升测试数学试题
6 . 已知函数
.
(1)若
,讨论
的单调性;
(2)若关于x的方程
有且只有一个解,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d26a7971fac9558a85695410bb9d8ba.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0a974c6dbd1b25e99411faec3732f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ae17be0d5d097ac8ff3832fbba75d4.png)
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解题方法
7 . 已知结论:椭圆
上一点
处切线方程为
.试用此结论解答下列问题.如图,已知椭圆
:
的右焦点为
,原点为
,椭圆的动弦AB过焦点
且不垂直于坐标轴,弦
的中点为
,椭圆
在点A,B处的两切线的交点为
.
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a271c22e34d4df61636ab3052a8e0ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1185a977aa9dc61d23db4b658126f8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/b9703fbb-7e2a-404b-bdfe-c1c16369ef43.png?resizew=161)
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfba099195b252ab0faba0d8360fae98.png)
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解题方法
8 . 一个圆被
轴分成两段,弧长之比为1:3,被
轴截得弦长为4,求圆心到直线
距离最小时圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934afdd41b042c53d1e54bc73a8713e3.png)
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9 . 已知椭圆
的上顶点为
,右焦点为
,原点
到直线
的距离为
的面积为1.
(1)求椭圆
的方程;
(2)过点
的直线
与
交于
两点,过点
作
轴于点
,过点
作
轴于点
与
交于点
.
①求证:点
在定直线上,
②求
的面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767a75d8d8add0ffa3db20e77797df31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b8452ffb321d5cf3887a129757b78e9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea91b1fb8690c09739e2981735f1919f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecde35e9255cb7922a86536b05f4a302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c217dadaca86779f03a2760377b6be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d8e33929752b1cb4dd36ee9b98b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
①求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
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10 . 设双曲线
的离心率为
,且顶点到渐近线的距离为
.已知直线
过点
,直线l与双曲线C的左、右两支的交点分别为M、N,直线l与双曲线C的渐近线的交点为P、Q,其中点Q在y轴的右侧.设
、
、
的面积分别是
、
、
.
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3c8091d78595c42d437ff5766431a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38be38165dc2307982fc57001a447c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633ca6abf0a23f7986facd5941edfe2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56b0348213284a19e2acc5a088fa491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a95ec3bb06756f0b4f047282de02bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb6540a11d075370516d9489066968d3.png)
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2024-03-01更新
|
298次组卷
|
3卷引用:湖南省常德市临澧县第一中学2023-2024学年高二下学期入学考试数学试题