1 . (1)证明:当
时,
;
(2)若过点
且斜率为
的直线
与曲线
交于
两点,
为坐标原点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3468ddff079eafd5b6062e230f8ed42a.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0482468ee9123843cc9310b1fd7a27b4.png)
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解题方法
2 . 远程桌面连接是一种常见的远程操作电脑的方法,除了windows系统中可以使用内置的应用程序,通过输入IP地址等连接到他人电脑,也可以通过向日葵,anyviewer等远程桌面软件,双方一起打开软件,通过软件随机产生的对接码,安全的远程访问和控制另一台电脑.某远程桌面软件的对接码是一个由“1,2,3”这3个数字组成的五位数,每个数字至少出现一次.
(1)求满足条件的对接码的个数;
(2)若对接码中数字1出现的次数为
,求
的分布列和数学期望.
(1)求满足条件的对接码的个数;
(2)若对接码中数字1出现的次数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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2024-03-31更新
|
1664次组卷
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4卷引用:海南省琼海市嘉积中学2023-2024学年高三下学期一模考试数学试题
海南省琼海市嘉积中学2023-2024学年高三下学期一模考试数学试题海南省四校(海南中学、海口一中、文昌中学、嘉积中学)2024届高三下学期联考数学试题(已下线)数学(全国卷理科01)(已下线)第七章:随机变量及其分布章末重点题型复习(7题型)-2023-2024学年高二数学同步精品课堂(人教A版2019选择性必修第三册)
3 . 某学校有甲、乙、丙三名保安,每天由其中一人管理停车场,相邻两天管理停车场的人不相同.若某天是甲管理停车场,则下一天有
的概率是乙管理停车场;若某天是乙管理停车场,则下一天有
的概率是丙管理停车场;若某天是丙管理停车场,则下一天有
的概率是甲管理停车场.已知今年第1天管理停车场的是甲.
(1)求第4天是甲管理停车场的概率;
(2)求第
天是甲管理停车场的概率;
(3)设今年甲、乙、丙管理停车场的天数分别为
,判断
的大小关系.(给出结论即可,不需要说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求第4天是甲管理停车场的概率;
(2)求第
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)设今年甲、乙、丙管理停车场的天数分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d8841d041817cc37743ba151c85a639.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86add0cc3a34f9d2a2e6afb78008c26.png)
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4 . 已知集合
,其中
都是
的子集且互不相同,记
的元素个数,
的元素个数
.
(1)若
,直接写出所有满足条件的集合
;
(2)若
,且对任意
,都有
,求
的最大值;
(3)若
且对任意
,都有
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13757649d1059dabada7fbafde58e6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96fa7b00ef7b8cf8e5a42aeb29f5154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf783a679243d115e602912050e47ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/775adbe6736b3ec038d45a4f209ac290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f71a52871eb36b27836d6b9d72029ac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/144e563700d35bb31aa51bab681f3118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cf86650443d1b86c79b1e3edc7e5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebd42fc2af57877e06f485b50ae4d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19eee6183061532e744ef9086ffcb8b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a245761c2403d38b654894e0c78cec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebd42fc2af57877e06f485b50ae4d87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27d4e5e05097560b51f888f8b234bc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-23更新
|
872次组卷
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4卷引用:海南省海南中学2024届高三下学期第九次半月考数学试题
5 . 某工厂有工人200名,统计他们某天加工产品的件数,统计数据如下表所示:
规定一天加工产品件数大于70的工人为“生产标兵”.已知这天的生产标兵中年龄大于30岁的有15人,这15人占该工厂年龄大于30岁的工人数的
.
(1)完成下面的
列联表,根据小概率值
的独立性检验,能否认为该工厂的工人是否为生产标兵与年龄有关?
(2)该工厂采用“阶梯式”的计件工资:日加工产品不超过50件的部分每件1元,超过50件但不超过60件的部分每件2元,超过60件但不超过80件的部分每件3元,超过80件的部分每件5元.假设工人小张每天加工产品的件数只可能为样本数据中各分组区间的右端点值,用对应区间的频率估计其概率,求小张每天的计件工资
(单位:元)的期望.
附:
.
加工产品的件数 | ![]() | ![]() | ![]() | ![]() | ![]() |
人数 | 50 | 80 | 40 | 20 | 10 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267c88e52743f3dedd4e60569cb958fe.png)
(1)完成下面的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead9d6ff51996f3ebace6f212e11a9e4.png)
年龄不大于30岁 | 年龄大于30岁 | |
生产标兵 | ||
非生产标兵 |
(2)该工厂采用“阶梯式”的计件工资:日加工产品不超过50件的部分每件1元,超过50件但不超过60件的部分每件2元,超过60件但不超过80件的部分每件3元,超过80件的部分每件5元.假设工人小张每天加工产品的件数只可能为样本数据中各分组区间的右端点值,用对应区间的频率估计其概率,求小张每天的计件工资
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acdae22187505cbfe595c3c31260d1cc.png)
![]() | 0.05 | 0.01 | 0.001 |
![]() | 3.841 | 6.635 | 10.828 |
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6 . 英国数学家泰勒发现了如下公式:
其中
为自然对数的底数,
.以上公式称为泰勒公式.设
,根据以上信息,并结合高中所学的数学知识,解决如下问题.
(1)证明:
;
(2)设
,证明:
;
(3)设
,若
是
的极小值点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6696028290bbaddf628d64bad0ed95b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2976d45a26ec77149a05553e8eb13efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78478b44ff22e088fd8e6522c5d78a2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d84ae7f43ef85da907d2917ff5f2a80.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8586154d8c4fb5fef893d39a7701f921.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde823e2e88ecb6045d66d61962259b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-03更新
|
2367次组卷
|
19卷引用:海南省海南华侨中学2023-2024学年高三下学期第二次模拟考试数学试题
海南省海南华侨中学2023-2024学年高三下学期第二次模拟考试数学试题贵州省贵阳市2024届高三下学期适应性考试数学试卷(一)贵州省安顺市2024届高三下学期模拟考试(一)数学试卷云南省玉溪市第一中学2023-2024学年高二下学期3月月考数学试题重庆市礼嘉中学2023-2024学年高二下学期第一次月考数学试题吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题重庆第十一中学校2023-2024学年高二下学期3月月考数学试题重庆市璧山中学校2023-2024学年高二下学期第一次月考数学试题广东省东莞市光明中学2023-2024学年高二下学期第一次月考数学试题四川省达州外国语学校2023-2024学年高二下学期3月月考数学试题黑龙江省哈尔滨市双城区兆麟中学2023-2024学年高二下学期第一次月考(4月)数学试题重庆市荣昌中学校2023-2024学年高二下学期4月期中考试数学试题广东省广州市广州中学2023-2024学年高二下学期期中考试数学试题江西省宜春市上高二中2024届高三下学期5月月考数学试卷(已下线)专题11 利用泰勒展开式证明不等式【练】河北省石家庄四十一中2023-2024学年高二下学期第一次月考数学试题河北省石家庄二中润德中学2023-2024学年高二下学期第一次月考数学试题福建省宁德市古田县第一中学2024届高中毕业班高考前适应性测试数学试题四川省南充市白塔中学2023-2024学年高二下学期期中考试数学试题
7 . 由
个数排列成
行
列的数表称为
行
列的矩阵,简称
矩阵,也称为
阶方阵,记作:
其中
表示矩阵
中第
行第
列的数.已知三个
阶方阵分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ff7824ff4c2d54281baa128c63235d.png)
,
,其中
分别表示
中第
行第
列的数.若
,则称
是
生成的线性矩阵.
(1)已知
,若
是
生成的线性矩阵,且
,求
;
(2)已知
,矩阵
,矩阵
是
生成的线性矩阵,且
.
(i)求
;
(ii)已知数列
满足
,数列
满足
,数列
的前
项和记为
,是否存在正整数
,使
成立?若存在,求出所有的正整数对
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f2dee59acd8ba55c25c9f5316ed3c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b540e0e8df1cc4f59180460e7d4264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ff7824ff4c2d54281baa128c63235d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39d394642b16525e70ecda2fd70cdb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0419a2c0acbb1af2d84373cca6d605a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d37e026f409868f81064617a4120e73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cbe82b97961a419f24e40bf54a1376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddff15b8d9a8b8f371670b3cba489b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62349070fb07aaeffbb5d7d91289a9.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab241dfd5146035044bc35dcfb3e0994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bb2b9e1f49aee4f4b91f0ba229fd75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b7d9aa89f698d7ac2772dbf24a5a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647c97da671781944dcbac93af7cadcb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4246c1e8163f564afaf51cec2352362e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ce6091ca3c6c454219a36f5396ccfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d03e28332446eea06a9bd61050d38373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c62349070fb07aaeffbb5d7d91289a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d7859dc8659a974ea86d14b6ef18e6.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c07cbe067882d2f964195527ad1b33c.png)
(ii)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7ffcaea39899aa3e4a17f9a5bc46f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b783cf91e34e692ce8e171f0965cb53f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd0bd4520a95ff89c01f5db5d0a0b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64d924836b4292239d9726c6473d7f5.png)
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8 . 已知动点
与定点
的距离和
到定直线
的距离的比为常数
.其中
,且
,记点
的轨迹为曲线
.
(1)求
的方程,并说明轨迹的形状;
(2)设点
,若曲线
上两动点
均在
轴上方,
,且
与
相交于点
.
①当
时,求证:
的值及
的周长均为定值;
②当
时,记
的面积为
,其内切圆半径为
,试探究是否存在常数
,使得
恒成立?若存在,求
(用
表示);若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d7a6fd6d651ae341154c2e40928d628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4988bd24f9af3f2b3c59aae61ca47ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be44077d42cfffece905b1af13e000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d812643e080d4d447fab7fe2ae2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ed21d7e90d10088ad597fca655100.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf2957b0a640070e941253e6d6d8be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba58e749d3c9f94abf0cc4743b8bc4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/207a808ffbeb016857125fbd530e0d5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7091d529281abff275ef19b9197445a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fdefb61da9119bdf6093ac2b9e7de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
您最近一年使用:0次
2024-02-29更新
|
5212次组卷
|
7卷引用:海南省海南中学2024届高三第一次模拟数学试题
海南省海南中学2024届高三第一次模拟数学试题广东省深圳市2024届高三第一次调研考试数学试卷(已下线)黄金卷08(2024新题型)广东省广州市白云中学2023-2024学年高三下学期零模(3月月考)数学试题2024届河北省承德市部分高中二模数学试题河北省衡水市部分学校2024届高三下学期二模考试数学试题(已下线)数学(新高考卷02,新题型结构)
名校
解题方法
9 . 如图1,在梯形
中,
,过
分别作梯形的高
,交
于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c739074553618fbb8d242ca53976384.png)
,沿
所在直线将梯形折叠,使得点
与点
重合,记为点
,如图2,M是
中点,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5214425d-ec5b-4e0a-821b-ddf877a78e21.png?resizew=355)
(1)证明:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)
是线段
上异于端点的一点,从条件①、条件②、条件③中选择一个作为已知,求平面
与平面
的夹角的余弦值.
条件①:
;
条件②:四棱锥
的体积为
;
条件③:点
到平面
的距离为
;
注:如果选择多个条件分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c739074553618fbb8d242ca53976384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40be06d1ee73fd02f0a6039081dc4c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5214425d-ec5b-4e0a-821b-ddf877a78e21.png?resizew=355)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a4dfcf4c24a8ecb210cc4c53db221.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d761129d39626d79053680475caba8.png)
条件②:四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504c7cd04dc84c872e5539d9906bd36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
条件③:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次