名校
解题方法
1 . 如图,在平面直角坐标系
中,双曲线
的上下焦点分别为
.已知点
和
都在双曲线上,其中
为双曲线的离心率.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/a6dc08c7-70f9-4daf-a3ef-ebeca0222160.png?resizew=167)
(1)求双曲线的方程;
(2)设
是双曲线上位于
轴右方的两点,且直线
与直线
平行,
与
交于点
.
(I)若
,求直线
的斜率;
(II)求证:
是定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdf3827864712be547ff16252f43baae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d2b272b441a87d2f253fae0b19eefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f5b0f68545a8d59361331bcb6c2b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481c543b01d90183de82d82433bfa49e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/6/a6dc08c7-70f9-4daf-a3ef-ebeca0222160.png?resizew=167)
(1)求双曲线的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(I)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2fda21bd0a804fcd893a65cefaa701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
(II)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762d2c5304d4b9a6867a359dbecb0956.png)
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2024-01-03更新
|
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3卷引用:江西省新余市第一中学2023-2024学年高二下学期开学考试数学试卷
名校
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dda8e0f05f65226b95a71bc0d75bc9.png)
(1)当
时,求函数
的极值;
(2)求函数
的单调区间;
(3)若对任意的实数
,函数
与直线
总相切,则称函数
为“恒切函数”.当
时,若函数
是“恒切函数”,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8dda8e0f05f65226b95a71bc0d75bc9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceee0ff5c929d67de3c294e027c9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a60550d48fcf76d109f426149d8185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0780bba5832fe480a5fddd87bd1af36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6077c98670d416a38f736c11f3591966.png)
您最近一年使用:0次
2023-12-20更新
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587次组卷
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4卷引用:北京市第八十中学2024届高三下学期开学考试数学试卷
名校
3 . 如图,已知
为半圆O的直径,点P为直径
上的任意一点.以点A为圆心,
为半径作
,
与半圆O相交于点C;以点B为圆心,
为半径作
,
与半圆O相交于点D,且线段
的中点为M.求证:
分别与
和
相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c20d0b44025a639ce3a92d639dae587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6f6558fef858bf27e9811c2d9426fe7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/25/d54dd79c-03d4-48a3-9f0f-f114e79b57bb.png?resizew=177)
您最近一年使用:0次
2023-07-22更新
|
70次组卷
|
2卷引用:浙江省杭州第二中学2022-2023学年高一上学期分班考数学试题
名校
解题方法
4 . 若集合A具有以下性质,则称集合A是“好集”:①
;②若
,则
,且
时,
.
(1)分别判断集合
,有理数集
是否是“好集”,并说明理由;
(2)设集合
是“好集”,求证:若
,则
;
(3)对任意的一个“好集”A,判断下面命题的真假,并说明理由;命题:若
,则必有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c9b39503b6484104862e21772b1431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03cb9923332c1afa835e98fa24e2f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46de01c5104b9112a688df37eadb000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd77104cc745d1e0e262122da34482d.png)
(1)分别判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a05551b1d4b65f27a932c33ddb1cb6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03cb9923332c1afa835e98fa24e2f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957d41dbe52b49c3a7339e3519a3fe84.png)
(3)对任意的一个“好集”A,判断下面命题的真假,并说明理由;命题:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e03cb9923332c1afa835e98fa24e2f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae4f0ccdfc1206d809e581449d0452e.png)
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名校
5 . 设函数
.
(1)证明:函数
在
上是增函数;
(2)若
是否存在常数
,使函数
在
上的值域为
,若存在,求出
的范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e28634b1106bf7698017b8c85d40a0c.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f05dd10ce64f773a0a676c5805077c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beea6fb7638645e13fe701fcf798fffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f68bca234d478ab4c052adf6193ab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
6 . 已知函数
.
(1)若
在
上单调递增,求实数
的取值范围;
(2)若
存在极小值,且极小值等于
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8240de29659c1bc859155b05eacb5826.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c6825734d355096bfdb6a451a69459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1a7ff645ecfe55a47581e14aacd3dc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5078b6d178b8225d61088752437e0b29.png)
您最近一年使用:0次
2023-01-18更新
|
815次组卷
|
4卷引用:湖南省株洲市第二中学2022-2023学年高二下学期入学考试数学试题
湖南省株洲市第二中学2022-2023学年高二下学期入学考试数学试题重庆市第一中学校2022-2023学年高二上学期期末数学试题(已下线)第五章 一元函数的导数及其应用章末检测卷(一)-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)(已下线)专题7 导数与极值点偏移【练】
名校
7 . 设函数
,其中
,若任意
均有
,则称函数
是函数
的控制函数”,且对于所有满足条件的函数
在
处取得的最小值记为
.
(1)若
,试问
是否为
的控制函数”;
(2)若
,使得直线
是曲线
在
处的切线,证明:函数
为函数
的控制函数,并求“
”的值;
(3)若曲线
在
处的切线过点
,且
,证明:当且仅当
或
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d0d9cf90ee9e4216f6c5e19f7f4d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cacd894a237683d42c389bfa5c27936c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecea80c2b9483e2c65d7572598a48dbd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d709d206efc9c004cf7ba5301aad67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94376e3e25de7fa4e506d40446b22ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55679c4d0d7c781f5db02eedb98baa4b.png)
(3)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fa12e23f7017e424166ba4622b0e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2023d0f4982eec32fae3b57bec6d8e31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436b2649162a1b61b6ef0ab2bda35bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7f7734539f4ceb08561cd4d1ecbc6.png)
您最近一年使用:0次
2023-01-08更新
|
815次组卷
|
5卷引用:上海市2023届高三下学期开学摸底数学试题
上海市2023届高三下学期开学摸底数学试题2023届上海春季高考练习上海市复旦大学附属中学青浦分校2022-2023学年高二下学期3月月考数学试题上海市闵行(文琦)中学2023-2024学年高二下学期3月月考数学试题(已下线)专题05导数及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)
名校
解题方法
8 . 已知拋物线
的焦点为
,过点
且斜率为
的直线
交
于
两点.当
时,
.
(1)求
的方程;
(2)若
关于
轴的对称点为
,当
变化时,求证:直线
过定点,并求该定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e041a52887466723ea61f8a373185218.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e733a15f50fdde9ac81ac1ce6e863f.png)
您最近一年使用:0次
2022-07-20更新
|
284次组卷
|
5卷引用:四川省泸县第四中学2022-2023学年高二下学期开学考试数学(理)试题
四川省泸县第四中学2022-2023学年高二下学期开学考试数学(理)试题四川省资阳市2021-2022学年高二下学期期末质量检测数学(理)试题四川省资阳市2021-2022学年高二下学期期末数学文科试题江苏省南京外国语学校2023-2024学年高二上学期10月月考数学试题(已下线)专题3-6 抛物线综合大题归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)
9 . 某数学课外活动小组在学习了勾股定理之后,针对图1中所示的“由直角三角形三边向外侧作多边形,它们的面积S1,S2,S3之间的关系问题”进行了以下探究:
(1)(类比探究)如图2,在Rt△ABC中,BC为斜边,分别以AB,AC,BC为斜边向外侧作Rt△ABD,Rt△ACE,Rt△BCF,若∠1=∠2=∠3,则面积S1,S2,S3之间的关系式为 ;
(2)(推广验证)如图3,在Rt△ABC中,BC为斜边,分别以AB,AC,BC为边向外侧作任意△ABD,△ACE,△BCF,满足∠1=∠2=∠3,∠D=∠E=∠F,则(1)中所得关系式是否仍然成立?若成立,请证明你的结论;若不成立,请说明理由;
(3)(拓展应用)如图4,在五边形ABCDE中,∠A=∠E=∠C=105°,∠ABC=90°,AB=2
,DE=2,点P在AE上,∠ABP=30°,PE=
,求五边形ABCDE的面积.
(1)(类比探究)如图2,在Rt△ABC中,BC为斜边,分别以AB,AC,BC为斜边向外侧作Rt△ABD,Rt△ACE,Rt△BCF,若∠1=∠2=∠3,则面积S1,S2,S3之间的关系式为 ;
(2)(推广验证)如图3,在Rt△ABC中,BC为斜边,分别以AB,AC,BC为边向外侧作任意△ABD,△ACE,△BCF,满足∠1=∠2=∠3,∠D=∠E=∠F,则(1)中所得关系式是否仍然成立?若成立,请证明你的结论;若不成立,请说明理由;
(3)(拓展应用)如图4,在五边形ABCDE中,∠A=∠E=∠C=105°,∠ABC=90°,AB=2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/17/e726fb38-d682-4354-a137-8b49d5325be4.png?resizew=756)
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10 . 如图,C是以
为直径的圆O上异于A,B的点,平面
平面
为正三角形,E,F分别是
上的动点.
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981598298152960/2982708857364480/STEM/1858a6bf-09bf-4f95-9ef2-bcd07ab7a52c.png?resizew=214)
(1)求证:
;
(2)若E,F分别是
的中点且异面直线
与
所成角的正切值为
,记平面
与平面
的交线为直线l,点Q为直线l上动点,求直线
与平面
所成角的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eafd509d9cc5c7618aee2967105364b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://img.xkw.com/dksih/QBM/2022/5/17/2981598298152960/2982708857364480/STEM/1858a6bf-09bf-4f95-9ef2-bcd07ab7a52c.png?resizew=214)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d05b5b9502c2be337f9be84fe4ed.png)
(2)若E,F分别是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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2022-05-19更新
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