名校
1 . 若数列
的各项均为正数,且对任意的相邻三项
,都满足
,则称该数列为“对数性凸数列”,若对任意的相邻三项
,都满足
则称该数列为“凸数列”.
(1)已知正项数列
是一个“凸数列”,且
,(其中
为自然常数,
),证明:数列
是一个“对数性凸数列”,且有
;
(2)若关于
的函数
有三个零点,其中
.证明:数列
是一个“对数性凸数列”:
(3)设正项数列
是一个“对数性凸数列”,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5323231f6376db726f6fba9dd53b97a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345367d7aac000974ce1e3cf4ce1b15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5323231f6376db726f6fba9dd53b97a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870910beaaf7bd60242701ad7ddaf06b.png)
(1)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a11176eb502db16e19c38278b77e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1e49907ec00414cee66b1d082183fb.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fe507c4d73de71c69ede4cfbdc7fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02ab7609f5b06fc564e8e588f378870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
(3)设正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5330adb65f6c8bd64d0cad579ad2910c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca2b0946db9bbcbce5f19507f5c485e.png)
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2 . “让式子丢掉次数”—伯努利不等式(Bernoulli’sInequality),又称贝努利不等式,是高等数学分析不等式中最常见的一种不等式,由瑞士数学家雅各布.伯努利提出,是最早使用“积分”和“极坐标”的数学家之一.贝努利不等式表述为:对实数
,在
时,有不等式
成立;在
时,有不等式
成立.
(1)证明:当
,
时,不等式
成立,并指明取等号的条件;
(2)已知
,…,
(
)是大于
的实数(全部同号),证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30cdfc52dbd70827de9e15fffe39c321.png)
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc98a4d9ae0580aa2c1152ffb770d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4fb8df3614557f13bdc68378437e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d4045366a437d4003259050718e244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f75f0daa973c8fc183b7d21bafd7e8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c78998ba5f2665a1753c3fa84751716.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc98a4d9ae0580aa2c1152ffb770d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5026dc5ead3b5adf0e5f4b3e7c4eca1d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1cc5cfec94bc5686b41b043acdc8ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30cdfc52dbd70827de9e15fffe39c321.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b29215b2a741c01efc27199e6c6925.png)
您最近一年使用:0次
2024-05-30更新
|
285次组卷
|
3卷引用:江西省鹰潭市2024届高三第二次模拟考试数学试卷
3 . 如图所示数阵,第
行共有
个数,第m行的第1个数为
,第2个数为
,第
个数为
,规定:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96a1efc782c7cbbbd7ccd55ae6c06c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442c68ee525e11e798702dcca3f4ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d80851ce143df1c3e1f7bd0bb28754d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8869622c406f60ca66f66cbf7e0f94cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c9cefa7564754d75af2709b98b559c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82123c3c62e343e06a547f58ea074bea.png)
…… … … … … …
(1)试判断每一行的最后两个数的大小关系,并证明你的结论;
(2)求证:每一行的所有数之和等于下一行的最后一个数;
(3)从第1行起,每一行最后一个数依次构成数列
,设数列
的前n项和为
是否存在正整数k,使得对任意正整数n,
恒成立?如存在,请求出k的最大值,如不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdd4f87e7e7e32d723d7e97d980db42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0623207595425920f16e76a7f8f268b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29a285201fd7e0ad70fa7431cb89a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0749c4129afc0c704155f522290b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae0b861522b18be1753acc4474cbc9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222268dda9dcb9b660f3cbedbb37757.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f1e3925bda80e8223bf7e431585847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96a1efc782c7cbbbd7ccd55ae6c06c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6442c68ee525e11e798702dcca3f4ac7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d80851ce143df1c3e1f7bd0bb28754d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8869622c406f60ca66f66cbf7e0f94cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c9cefa7564754d75af2709b98b559c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82123c3c62e343e06a547f58ea074bea.png)
…… … … … … …
(1)试判断每一行的最后两个数的大小关系,并证明你的结论;
(2)求证:每一行的所有数之和等于下一行的最后一个数;
(3)从第1行起,每一行最后一个数依次构成数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23e8660fb54ba32b037b392b75316087.png)
您最近一年使用:0次
4 . 已知各项均不为0的数列
满足
(
是正整数),
,定义函数
,
是自然对数的底数.
(1)求证:数列
是等差数列,并求数列
的通项公式;
(2)记函数
,其中
.
(i)证明:对任意
,
;
(ii)数列
满足
,设
为数列
的前
项和.数列
的极限的严格定义为:若存在一个常数
,使得对任意给定的正实数
(不论它多么小),总存在正整数m满足:当
时,恒有
成立,则称
为数列
的极限.试根据以上定义求出数列
的极限
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39bf7b5dc247fe10b6bfd984413a5e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd9ea8ffdea8c77370ea3e5f563dc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51fec2729d8e927de9392ee90d1e0389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6f0a55fa53bf5f8e6654897975bcf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3324481138f2dc750f9ad889054abe1.png)
(i)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416a72de4d0030203a867cc3b7b95d83.png)
(ii)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0857559ed421cc7c614708f34f9f3324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad481cbfb67ac9cdbc0537f3de23b022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/856b137a34d2d5b20671b7a3c7a29606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9de1835c164233db8b623489fbda0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
名校
5 . n个有次序的实数
,
,…,
所组成的有序数组
称为一个n维向量,其中
称为该向量的第i个分量.特别地,对一个n维向量
,若
,称
为n维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在10个两两垂直的10维信号向量;
(3)已知k个两两垂直的2024维信号向量
,
,…,
满足它们的前m个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa87d9662032c4b53e41634f3424b0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d5cd21ff3c760e7ec3130f5bfa8c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94fcc44ac04f54d5fcc1a6154b8b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d5cd21ff3c760e7ec3130f5bfa8c91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a414d372b680499f1c8ca1a7ae5f4d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cfee5ec6cb12cb32e04de5c387a2c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e45b1c120de76ab330bf5e9cb98cce.png)
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在10个两两垂直的10维信号向量;
(3)已知k个两两垂直的2024维信号向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9541e55ef7917c4d5eec7e5062a6f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0de4fe4539ececcc2452bea1046c7148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c3f353a2ff4a61f8b81a3314c09e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
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6 . 若数列
满足:存在等差数列
,使得集合
元素的个数为不大于
,则称数列
具有
性质.
(1)已知数列
满足
,
.求证:数列
是等差数列,且数列
有
性质;
(2)若数列
有
性质,数列
有
性质,证明:数列
有
性质;
(3)记
为数列
的前n项和,若数列
具有
性质,是否存在
,使得数列
具有
性质?说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48dfe427f8841f24337b83a767750352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5b653a209622a9136a15c3b11b0a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87e0860e3f142e7ddd7b45c16b211fa.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f24ba3195cbf220d03a1ef5bfe954f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde3c47074b6f1b16af81c3684d04419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e196cf353f8f832f24be4951a9fefab8.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d16238329f13aeeb2d13aaf025ba07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662422cae5190af5fa05475a1e16f2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b211310c6b436c4b7c4f38ce483d9b13.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763b41172fa5f9f9ef85ab59df78bc39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de777c4e44546bcfe26ad5b6bb418052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e87e0860e3f142e7ddd7b45c16b211fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/763b41172fa5f9f9ef85ab59df78bc39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b7006e157c36d567488d1c30936700.png)
您最近一年使用:0次
2024-04-10更新
|
445次组卷
|
3卷引用:河南省信阳市新县高级中学2024届高三下学期适应性考试(十)数学试题
名校
解题方法
7 . 已知
,
.
(1)求
在
上的最小值;
(2)求曲线
在
处的切线方程
,并证明:
,都有
;
(3)若方程
有两个不相等的实数根
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b6a91900d0dfa6296cdee22fdd6fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea17ec8f211e8be2571fbcce23e04eb8.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23a03ca8f1729bfcadf513784817fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3add1679c27392a1a7f635723a4b36eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8013645996eb5766aaf7de48d243d1de.png)
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名校
8 . 已知曲线
在点
处的切线为
.
(1)求直线
的方程;
(2)证明:除点
外,曲线
在直线
的下方;
(3)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1026c00ff9d78946b4984d09de77995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f84134092f31767ff9f7e8200a79fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:除点
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa83d5be9b28fcfce25c9bfca0d3d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab873c4173a3992c043fbf32cab4d8c.png)
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2024-04-26更新
|
1297次组卷
|
4卷引用:安徽省合肥市2024届高三第二次教学质量检测数学试卷
9 .
个有次序的实数
所组成的有序数组
称为一个n维向量,其中
称为该向量的第
个分量.特别地,对一个n维向量
,若
,
,称
为n维信号向量.设
,则
和
的内积定义为
,且
.
(1)写出所有3维信号向量;
(2)直接写出4个两两垂直的4维信号向量;
(3)证明:不存在14个两两垂直的14维信号向量;
(4)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2b043b989216035c6fd985f1dd6a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97de4e0337716e1d89eb1a6cfd7b8335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e51ca089ee13a138e985e20f1b7b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43d0d6f87afa8b4fd5f6cf81f2bdcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da796531c7b6c590a22b811df1fcef53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/293e6a784d135c77e3bded6f48f6eec9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6be373930634c9aa53fec30bec8896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2978e42bc0f5abe31fe2536969afa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)写出所有3维信号向量;
(2)直接写出4个两两垂直的4维信号向量;
(3)证明:不存在14个两两垂直的14维信号向量;
(4)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cae65660b220cc622b87ed9eea092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
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10 . 已知抛物线
上任意一点
满足
的最小值为
(
为焦点).
(1)求
的方程;
(2)过点
的直线经过
点且与物线交于
两点,求证:
;
(3)过
作一条倾斜角为
的直线交抛物线于
两点,过
分别作抛物线的切线.两条切线交于
点,过
任意作一条直线交抛物线于
,交直线
于点
,则
满足什么关系?并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac78092eec8d674c97589a30d687d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd1ac4958d35abc7a64812eca930d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5480c2dd9197e86d1989e70347f.png)
(3)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.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/4be563ee0cc1e5fe5abade7efbeda6a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a481f48bd003009e85fd18cc7e34ebe.png)
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