解题方法
1 . 抛掷一枚不均匀的硬币,正面向上的概率为
,反面向上的概率为
,记
次抛掷后得到偶数次正面向上的概率为
,则数列
的通项公式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
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解题方法
2 . 已知双曲线
的两条渐近线分别为
和
,右焦点坐标为
为坐标原点.
(2)直线
与双曲线的右支交于点
(
在
的上方),过点
分别作
的平行线,交于点
,过点
且斜率为4的直线与双曲线交于点
(
在
的上方),再过点
分别作
的平行线,交于点
,这样一直操作下去,可以得到一列点
.
证明:①
共线;
②
为定值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4073d527d4b14759a7cbaeabfb35a756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9fc68d6d88485e65bfc599dfdde547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c388c5a37852ee8ea1066ce1f9c1d5dd.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81337e2e2dbdd0c3148454fa41d44144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c7d2c85e7878b6cbfb45b71ffb60b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c7d2c85e7878b6cbfb45b71ffb60b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ca7a25d804f483ec024c735c633e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8357bec2e11a9f9756cd7c7e9143afca.png)
证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db4fe79b98486f0d4556f37d64d74f9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeda3264e04e2d3ed2a15c69adad05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dd9cb5cac04bc15c02f292b38d2928.png)
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3 . 数列极限理论是数学中重要的理论之一,它研究的是数列中数值的变化趋势和性质.数列极限概念作为微积分的基础概念,它的产生与建立对微积分理论的创立有着重要的意义.请认真理解下述3个概念.
概念1:对无穷数列
,称
为数列
的各项和.
概念2:对一个定义域为正整数集的函数
,如果当
趋于正无穷大时,
的值无限趋近于一个常数
,即当
时,
,就说常数
是
的极限值,记为
.如:
,当
时,由反比例函数的性质可知
,即记为
.当
(
为常数)时,
.
概念3:对无穷数列
,其各项和为
,若当
时,
(
为常数),即
,则称该数列的和是收敛的,
为其各项和的极限;若当
时,其各项和
的极限不存在,则称该数列的和是发散的,其各项和的极限不存在.
试根据以上概念,解决下列问题:
(1)在无穷数列
中,
,求数列
的各项和
的极限值;
(2)在数列
中,
,讨论数列
的和是收敛的还是发散的;
(3)在数列
中,
,求证:数列
的和是发散的.
概念1:对无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c434a9e76de70c0af36c324e1fd48d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
概念2:对一个定义域为正整数集的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4136968179e01108272af01324034127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e345e86daf74312a6992e5d1c3f47f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6784211a2342d9d829bd95e15b549b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e345e86daf74312a6992e5d1c3f47f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0057f1742dc20e867bcbc29e6475773a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40cd74412213ddb92f6b4637888cf3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cfc53624067d3c8e01f09361295dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc76422aeaa304648c34cd1c6c0674e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4eb29a351c1efa18e8e45d083491df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/961ea9a98e63ba37f650fde96c774026.png)
概念3:对无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06ea1200f943f6eb160b49e584b4335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f614310a33734a2d82f0d84c627028e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cb2108952d47acb4f0a9518cbef443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b06ea1200f943f6eb160b49e584b4335.png)
试根据以上概念,解决下列问题:
(1)在无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5beb1d3014af78f347ea9cf3661881cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccecde965d7557d5ee35dea8ae7164a3.png)
(2)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1111d85a7c8b1842e38b5d59da90954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(3)在数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f34f1354aaa4fa27de5215098e0b1e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
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名校
4 . 已知函数
.
(1)判断并证明
的零点个数
(2)记
在
上的零点为
,求证;
(i)
是一个递减数列
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ae99833cb675e5e36c58f345eb03e7.png)
(1)判断并证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64af919a56a107e0fc0a417e481648.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d64af919a56a107e0fc0a417e481648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167f4f8fd4d3de714b87f05e57a3ba3b.png)
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2024-06-04更新
|
511次组卷
|
2卷引用:河南省许昌市魏都区许昌高级中学2024届高三下学期5月月考数学试题
名校
5 . 下列不等式中正确的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-06-02更新
|
199次组卷
|
2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
解题方法
6 . 已知函数
.
(1)求函数
在区间
上的极值点的个数.
(2)“
”是一个求和符号,例如
,
,等等.英国数学家布鲁克·泰勒发现,当
时,
,这就是麦克劳林展开式在三角函数上的一个经典应用.
证明:(i)当
时,对
,都有
;
(ii)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa05afe3090417768122ef5a715419d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4fd84394e897ebf6c4814b841d427b.png)
(2)“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9e0e182953b1bbb73799d448ce65ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b6e1a20beab975ff39ef016e7c38a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d46ea45f17393046e9b82c3bce8a2c.png)
证明:(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a107eb946e0fe41629c644b7628d5cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad374f26bd25373e78b0999de68705ce.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fedf2798cbb949971b44f0a2314e67.png)
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7 . 已知
为单调递增的正整数数列,给定整数
,若存在不全为0的
,使得
,则称
为
阶
维表示数.
(1)若
,求
的通项公式,判断2024是否为3阶3维表示数,并说明理由;
(2)已知
,是否存在
,使得
同时是0阶
维表示数,1阶
维表示数,…,
阶
维表示数.若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ebe66a811dcb283966bc22d2b043de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03ddd6684996ab3f44d44dd011c3f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce2ee6c806563be3d0ef8aa30dff800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/5aadf9ab510510120699c5eee39ab18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7230bf66bd47039e759f48af51930ac.png)
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名校
8 . 若集合
,集合
,其中
,则称集合
是集合
的一个“
元子集”.若“
元子集”
中的元素
满足对任意
,恒有
,则称
为
的一个“个性独立子集”.已知集合
,集合
是
的一个“个性独立子集”.
(1)求所有满足条件的集合
的个数;
(2)若
且互不相等,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b7c647eb8e6be44689333e1a6f1f8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473ed4e9293f5066fe367cfa541afa11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d87fa699e2aca137f69e4ac0883dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a4aecf0b7edfa826f73389322a52cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f2c01531dd639f0ad3da0098febbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effaffc8a4d01f865a79933d3c337060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)求所有满足条件的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab3fa353ea21d2dea55e32a354e3dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0736f73b81bec1c5d4efe968cfbe2a.png)
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名校
9 . 孟德尔在观察豌豆杂交时发现了以下规律:豌豆的各种性状是由其遗传因子决定的. 以子叶颜色为例,豌豆的子叶分黄、绿两种颜色,其中黄色为显性性状,绿色为隐性性状. 我们用
表示子叶为黄色的豌豆的遗传因子对,用
表示子叶为绿色的豌豆的遗传因子对. 当这两种豌豆杂交时,父本的其中一个遗传因子与母本的其中一个遗传因子等概率随机组合,子一代的遗传因子对全部为
,如图所示,其中
为显性遗传因子,
为隐性遗传因子. 当生物的遗传因子对中含有显性遗传因子时呈现显性性状,否则呈现隐性性状. 例如:
均指示黄色子叶,
指示绿色子叶. 我们称以上定律为孟德尔定律.
与
)进行交配得到子三代豌豆,求子三代豌豆中子叶颜色为绿色的概率.
(2)已知人的单、双眼皮性状服从孟德尔定律,其中双眼皮是显性性状,记其遗传因子对为
或
;单眼皮是隐性性状,记其遗传因子对为
. 若仅考虑眼皮性状,已知你的祖父、祖母和母亲的遗传因子对均为
:
(ⅰ)在你是双眼皮的条件下,求父亲是单眼皮的概率;
(ⅱ)祖父和祖母育有伯父、父亲、叔父和姑母三子一女,除父亲外,其余三人均与单眼皮配偶婚配并各育有一子,求你及你的三代以内父系亲属(如图)中双眼皮人数的数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a9bdde17eba7e522d1e3850171a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b012d39bca448ca6d2f2563095af11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e122c4ec85171d39684543de1484b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b51c2660cbc2a1d78e3f00dd91d9a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b012d39bca448ca6d2f2563095af11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a9bdde17eba7e522d1e3850171a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a9bdde17eba7e522d1e3850171a85.png)
(2)已知人的单、双眼皮性状服从孟德尔定律,其中双眼皮是显性性状,记其遗传因子对为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c56378a35ea2dc824e60450356eba4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdacfce5b9dc683d4f742b3aad24c22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2441066b8a4db9e679e4ef61ecf1da4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdacfce5b9dc683d4f742b3aad24c22b.png)
(ⅰ)在你是双眼皮的条件下,求父亲是单眼皮的概率;
(ⅱ)祖父和祖母育有伯父、父亲、叔父和姑母三子一女,除父亲外,其余三人均与单眼皮配偶婚配并各育有一子,求你及你的三代以内父系亲属(如图)中双眼皮人数的数学期望.
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解题方法
10 . 如图,在平面直角坐标系
中,椭圆
与抛物线
交于第一象限的点
,过点
作抛物线的切线
交椭圆于另一点
,直线
交椭圆于另一点
,且满足
.
的离心率
;
(2)若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c118b51ab426bc1c1b56179094f146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b527ec9f92467b8f24554a2a67ee987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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