解题方法
1 . 如图,在四棱锥
中,底面
为菱形,
,
,
,
平面
,点M,N,H分别在棱PB,PD,PC上,且
.
;
(2)连接AC交BD于点O,连接OP.求证:
平面
;
(3)若H为PC的中点,PA与平面
所成角为60°,四棱锥
被平面
截为两部分,记四棱锥
体积为
,另一部分体积为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb96e0331eebe80ed1ff610faf531fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd68fe22ed9909165aedc98d1d8e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828247a3338571cb0d4ba2a5bf88929c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec6297cf195e60fd53375a501deb2ac.png)
(2)连接AC交BD于点O,连接OP.求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)若H为PC的中点,PA与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd68fe22ed9909165aedc98d1d8e3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bb075576cc0f585bda44277ac1d098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
您最近一年使用:0次
名校
2 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线,1691年,莱布尼茨等得出“悬链线”方程
,其中
为参数.当
时,就是双曲余弦函数
,类似的我们可以定义双曲正弦函数
.它们与正、余弦函数有许多类似的性质.
(1)求证:
;
(2)对
,不等式
恒成立,求实数
的取值范围;
(3)若
,试比较
与
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08144630f70f5bba0c73252569d97841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d848439a448faa1d4cd9fa20ca206215.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe0a24e9c7616bf8afac5a0ffb0aa1fb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdd3fb4f930b309f261929ba7a1f055.png)
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe9f3099ed9429dc5b4e38a350e524a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24464f0ea26038d85cc22a1786257605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a83c8948a168ff2c567aee048cabff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2cebaab3423dfb2f2c944dfc43df8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb966b7b2dd6581640bcee2d97dacf77.png)
您最近一年使用:0次
3 . 已知动圆
经过定点
,且与圆
:
内切.
(1)求动圆圆心
的轨迹
的方程;
(2)设轨迹
与
轴从左到右的交点为
,
,点
为轨迹
上异于
,
的动点,设
交直线
于点
,连接
交轨迹
于点
,直线
,
的斜率分别为
,
.
①求证:
为定值;
②证明:直线
经过
轴上的定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866502435d9ea08c6d3a5e304a8986c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8387b687579c4d5152175c9d19e24232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9811dd726ed27d28ad5a8e83fbb20ed6.png)
(1)求动圆圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30513ea48bc1ef3ae78adac83d894f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef79861421b414b455a090a3ef04fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b51a4949896526cfc3c076ea8dec8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128147bd4834566a78b4e9d2a3b2139c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb4a51e6728d354cc1c3d32e2d4368d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d727db2181aca4e8a6455d10cfe28.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6b1769274eee3ce2896cb3513d50f8.png)
②证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e430f13f42cf2d44aa0f0e20b959684f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-01-11更新
|
630次组卷
|
11卷引用:四川省泸州市泸县第一中学2024届高三上学期期末数学(理)试题
4 . ①在微积分中,求极限有一种重要的数学工具——洛必达法则,法则中有一结论:若函数
,
的导函数分别为
,
,且
,则
;
②设
,k是大于1的正整数,若函数
满足:对任意
,均有
成立,且
,则称函数
为区间
上的k阶无穷递降函数.
结合以上两个信息,回答下列问题:
(1)证明
不是区间
上的2阶无穷递降函数;
(2)计算:
;
(3)记
,
;求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ceac3910b9f134bab0b92e8d9a9eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74acc4d2f565d7088e8d737718e89602.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0c1abf0378a7f5d79672f622b275e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e54d86850a733707433da2e423a5c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580f20b900b6d8c9e90c84a0588ae74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3e441923ed3c1a32720d6aeac2f599.png)
结合以上两个信息,回答下列问题:
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d1f6f459292de1002f863203ce91a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
(2)计算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8063898825e02107b7e04f6eba28cb8c.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602d05de8ada4a6f4d53bab28430f684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d40b0c4fd043d372c463db08659e779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caea9a696f22c76f8f4563ac45d124b1.png)
您最近一年使用:0次
2024-04-18更新
|
458次组卷
|
6卷引用:四川省广安市华蓥中学2023-2024学年高二下学期4月月考数学试题
四川省广安市华蓥中学2023-2024学年高二下学期4月月考数学试题广东省广州市天河中学高中部2023-2024学年高二下学期基础测试数学试题(已下线)模块五 专题5 全真拔高模拟5(人教B版高二期中研习)广东省广州市天河中学2023-2024学年高二下学期第二次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5月期中考试数学试题(已下线)专题14 洛必达法则的应用【练】
名校
5 . 已知,图中直棱柱
的底面是菱形,其中
.又点
分别在棱
上运动,且满足:
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/98dca3c6-4024-46c7-bc8f-98f979981404.png?resizew=158)
(1)求证:
四点共面,并证明
平面
;
(2)是否存在点
使得二面角
的余弦值为
?如果存在,求出
的长;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa102f519d541f2e4d10a8975a41c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360a93b9662f0ab8a69b131497520b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626db48efbecf4e318252ba13baff47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1357d24d53b523a55b3eea7b21fa16f1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/98dca3c6-4024-46c7-bc8f-98f979981404.png?resizew=158)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51c4a1148587943fe9ba210f6141ee.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e807172fa9eca2416f92f341adc06165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
名校
解题方法
6 . 若函数
满足:对任意的实数
,
,有
恒成立,则称函数
为 “
增函数” .
(1)求证:函数
不是“
增函数”;
(2)若函数
是“
增函数”,求实数
的取值范围;
(3)设
,若曲线
在
处的切线方程为
,求
的值,并证明函数
是“
增函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9cec0474c43086ea39cb457048313c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dca031c9a6a1199cfee4c3d91c52099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b34671abe25726a52a57850ab248fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974f122681f314e8202e02861cabf8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916ae6490922319a1d394fbedd8d951a.png)
您最近一年使用:0次
2023-12-21更新
|
736次组卷
|
6卷引用:四川省屏山县中学校2023-2024学年高二下学期第一次阶段性考试数学试题
四川省屏山县中学校2023-2024学年高二下学期第一次阶段性考试数学试题(已下线)上海市奉贤区2024届高三一模数学试题变式题16-21重庆市育才中学校2023-2024学年高二下学期三月拔尖强基联盟联合考试巩固测试数学试题(已下线)上海市高二下学期期末真题必刷03(常考题)--高二期末考点大串讲(沪教版2020选修)上海市奉贤区2024届高三一模数学试题(已下线)拔高点突破05 函数与导数背景下的新定义压轴解答题(九大题型)
名校
解题方法
7 . 如图,四棱锥
中,
,
,E为PB的中点.
平面PAD;
(2)过D点是否存在一个与PA,AB相交,且与平面PBC平行的平面?若存在,指出交点位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4031f4aae0b996ce8fec956fb2879f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f30e54bb771ad15067221459f202f01.png)
(2)过D点是否存在一个与PA,AB相交,且与平面PBC平行的平面?若存在,指出交点位置,并证明你的结论;若不存在,请说明理由.
您最近一年使用:0次
2022-05-04更新
|
986次组卷
|
5卷引用:四川省南充市嘉陵第一中学2023-2024学年高一下学期第三次月考数学试卷
8 . 已知数列
中,
,
(
).
(1)证明:数列
是等比数列,并求
前
项的和
;
(2)令
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6c286f0bf939f0ec7abed0d75f414c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6274da8ba98281c221636aa0fb821f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0a11035037cfd4240c48bc89661374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d323cd4084e2553fcf29481373d0f65.png)
您最近一年使用:0次
2021-02-07更新
|
2119次组卷
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5卷引用:四川省南充高级中学2023-2024学年高二下学期第一次月考(3月)数学试题
四川省南充高级中学2023-2024学年高二下学期第一次月考(3月)数学试题浙江省绍兴市嵊州市2020-2021学年高三上学期期末数学试题(已下线)【新东方】绍兴数学高三上【00006】(已下线)精做01 数列-备战2021年高考数学大题精做(新高考专用)(已下线)2021年高考数学押题预测卷(江苏专用)02
9 . 如图,在多面体
中,
为等边三角形,
,
,
,点
为边
的中点.
平面
.
(2)在
上找一点
使得平面
平面
,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86652f9864f608ce96b993d196386ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53238eab89f2e272985b24e4cbdb5397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
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2020-01-03更新
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842次组卷
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7卷引用:四川省德阳市绵竹中学2023-2024学年高一下学期第三次(6月)月考数学试题
解题方法
10 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)若
恒成立,求
的取值范围;
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/536d662ffb82903b39d82d7053aadd2f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302337058242c7b78e3eb4ac7210b7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db40d5295942e85ec07a3728c7ad308d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b0c3cf87f438d1fe0f6fca51b40be2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e75f547129d14ffb61324fb58492ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db9ea9575be1bdcd679099b47e45c23.png)
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