解题方法
1 . 某学校组织竞赛,有A,B,C三类问题可供选择,其中A问题答对可得5分,答错0分,B问题答对只可得3分,但答错只有2分,C问题答对得4分,答错0分,现小明与小红参加此竞赛,小红答对3种问题的概率均为0.5,小明答对A,B,C问题的概率分别为0.3,0.7,0.5.
(1)小红一共参与回答了3题,且该
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(2)小明也参与回答了3道问题,3道问题可以是同一类,也可以不是同一类,记Y为小明的累计得分,求该如何分配问题,使得E[Y]最大.
您最近一年使用:0次
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2 . 已知
为正整数,对于给定的函数
,定义一个
次多项式
如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18970eb9afce70d15d8b276535427df2.png)
(1)当
时,求
;
(2)当
时,求
;
(3)当
时,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18970eb9afce70d15d8b276535427df2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28638f8c054a7bb4d9b46fde330bc76f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e44284cb19805a584880a686ac3df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c64d8ccd22b77a2b30da084d30d2e04.png)
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解题方法
3 . 已知
六个字母以随机顺序排成一行,若小明每次操作可以互换2个字母的位置,则小明必须进行5次操作才能将六个字母排成
的顺序的排列情况有______ 种.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63a98f5ed97655875ffb3f9eb413d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
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2023-05-11更新
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1146次组卷
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4卷引用:上海市上海中学2022-2023学年高二下学期期中数学试题
上海市上海中学2022-2023学年高二下学期期中数学试题上海市松江区华东政法大学附属松江高级中学2023-2024学年高二下学期3月月考数学试题(已下线)专题06计数原理--高二期末考点大串讲(沪教版2020选修)(已下线)第一章 排列组合与二项式定理 专题一 两个计数原理 微点1 分类加法计数原理与分步乘法计数原理【培优版】
名校
解题方法
4 . 若
,则下列结论中正确的有_____ .
①若
为整数,则
;
②
是正整数;
③
是
的小数部分;
④设
,若
、
为整数,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0b21dddd3765821613ded382d13d6e.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaad2cc1f9365f649b4d6632e6e8f8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0df4e2a02814376fdfeea2aabdef0d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c81f436cc2175c4bcb5a6e9d92ae6c.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d9c6b518711638e215d4f01926051e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d9eafe185f2abaa3520b6b540ad0ced.png)
④设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682b100b6961e679fe8800e818b2c2a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59e7c7a84a4bdb959e95536d0404ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e260b088f071983f254ce8f5163fcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f5769b222b4fb6b177144105c332fa.png)
您最近一年使用:0次
2022-12-30更新
|
807次组卷
|
5卷引用:上海市大同中学2022届高三下学期期中数学试题
上海市大同中学2022届高三下学期期中数学试题(已下线)6.5二项式定理(分层练习)-2022-2023学年高二数学同步精品课堂(沪教版2020选择性必修第二册)(已下线)第6章 计数原理(基础、常考、易错、压轴)分类专项训练-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)四川省雅安市天立学校2022-2023学年高二下学期第一次月考数学(理)试题
名校
解题方法
5 . 现要将一边长为101的正方体
,分割成两部分,要求如下:(1)分割截面交正方体各棱
,
,
,
于点P,Q,R,S(可与顶点重合);(2)线段
,
,
,
的长度均为非负整数,且线段
,
,
,
的每一组取值对应一种分割方式,则有___________ 种不同的分割方式.(用数字作答)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b81f1bce5be292fb6968afc5e07864f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb6fd2fa53b92a03d21f208b74e3857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b81f1bce5be292fb6968afc5e07864f.png)
您最近一年使用:0次
2022-06-22更新
|
1999次组卷
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2卷引用:上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题
6 . 设集合
,其中
,
,在M的所有元素个数为K(
,2≤K≤n)的子集中,我们把每个K元子集的所有元素相加的和记为
(
,2≤K≤n),每个K元子集的最大元素之和记为
(
,2≤K≤n),每个K元子集的最小元素之和记为
(
,2≤K≤n).
(1)当n=4时,求
、
的值;
(2)当n=10时,求
的值;
(3)对任意的n≥3,
,给定的
,2≤K≤n,
是否为与n无关的定值?若是,请给出证明并求出这个定值:若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8aa469da8a950d471de1ab21529b7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca2f42085784f69dce4d8df6c2751cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6b7d9861f405144acc112dbaa83719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d109d041d18da77fa4bc8e8df8513d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
(1)当n=4时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(2)当n=10时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2114a0fe21dc0e5bf831c146ef02b113.png)
(3)对任意的n≥3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7a3c9c8561ec934c904389b712fcf.png)
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7 . 某校高二年级共有10个班级,5位教学教师,每位教师教两个班级,其中姜老师一定教1班,张老师一定教3班,王老师一定教8班,秋老师至少教9班和10班中的一个班,曲老师不教2班和6班,王老师不教5班,则不同的排课方法种数______ .
您最近一年使用:0次
2021-03-22更新
|
3216次组卷
|
7卷引用:上海市华东师范大学第二附属中学2022-2023学年高二下学期期末数学试题
(已下线)上海市华东师范大学第二附属中学2022-2023学年高二下学期期末数学试题(已下线)专题06计数原理--高二期末考点大串讲(沪教版2020选修)黑龙江省哈尔滨市第三中学2020-2021学年度上学期高二学年第二模块考试(理科)数学试题(已下线)第6章 计数原理(新文化与压轴30题专练)2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)专题10-1 排列组合20种模型方法归类-4(已下线)6.2.1排列-6.2.2排列数——课时作业(提升版)(已下线)6.2.1排列-6.2.2排列数——课时作业(巩固版)
名校
解题方法
8 . 某地计划在水库建一座至多安装3台发电机的水电站.过去50年的水文资料显示,水库年入流量
(年入流量:一年内上游来水与库区降水之和.单位:亿立方米)都在40以上,其中,不足80的年份有10年,不低于80且不超过120的年份有35年,超过120的年份有5年,将年入流量在以上三段的频率作为相应段的概率,并假设各年的年入流量相互独立.
(1)求未来4年中,至多有1年的年入流量超过120的概率;
(2)水电站希望安装的发电机尽可能运行,但每年发电机最多可运行台数受年入流量
限制,并有如下关系:
若某台发电机运行,则该台发电机年净利润为5000万元;若某台发电机未运行,则该台发电机年维护费与年入流量
有如下关系:
欲使水电站年净利润最大,应安装发电机多少台?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求未来4年中,至多有1年的年入流量超过120的概率;
(2)水电站希望安装的发电机尽可能运行,但每年发电机最多可运行台数受年入流量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
年入流量 | |||
发电机最多可运行台数 | 1 | 2 | 3 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
年入流量 | ||
一台未运行发电机年维护费 | 500 | 800 |
您最近一年使用:0次
2020-05-15更新
|
1083次组卷
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3卷引用:上海市闵行(文绮)中学2023-2024学年高三下学期5月月考数学试卷
9 . 两个数列
、
,当
和
同时在
时取得相同的最大值,我们称
与
具有性质
,其中
.
(1)设
的二项展开式中
的系数为
(
),
,记
,
,
,依次下去,
,组成的数列是
;同样地,
的二项展开式中
的系数为
(
),
,记
,
,
,依次下去,
,组成的数列是
;判别
与
是否具有性质
,请说明理由;
(2)数列
的前
项和是
,数列
的前
项和是
,若
与
具有性质
,
,则这样的数列
一共有多少个?请说明理由;
(3)两个有限项数列
与
满足
,
,且
,是否存在实数
,使得
与
具有性质
,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728d33987f271f5ec625592076593b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d032d57e0d95dddb3d4501249f1327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728d33987f271f5ec625592076593b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d032d57e0d95dddb3d4501249f1327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca4f2b82d9d7a8323c8d697338a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728d33987f271f5ec625592076593b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d032d57e0d95dddb3d4501249f1327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5839a256b56cb644d8a76fa40da0f339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce733aaa0bf65084fedbf529da36ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e668f6e2cbdb731bac88892e47fddf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e10f2f74e201f77f853e9ed9078615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8140a39887c6b0b3f26b226c090a3127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78908ea2f65b1af56be13743cf5c3faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf87d2d47a420aee5be760a6de0d3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a28198a932f4f9a93a4c613bbc2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce733aaa0bf65084fedbf529da36ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e668f6e2cbdb731bac88892e47fddf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e10f2f74e201f77f853e9ed9078615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0f8b318bae5924c4d2b0194946f259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54d77d1248bbd1398a828a3389ce78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba468c3d2d7b3fa8e65885bfacf4a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21ab17f8694a07cfcc9e63389b34690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5d0896cc32b7f445c3dab320482515.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/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81decee0ccfa372af8951ca73ada38a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21ab17f8694a07cfcc9e63389b34690.png)
(3)两个有限项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043d21c4badb8e2bd98390c7f1c25822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b3cf64372426d1d2faff63d34fdcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
10 . 规定:对于任意实数
,若存在数列
和实数
,使
,则称
可以表示成
进制形式,简记为:
;如:
,表示
是一个2进制形式的数,且
;
(1)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
,试将
表示成
进制的简记形式;
(2)若数列
满足
,
,
,
,
,求证:
;
(3)若常数
满足
且
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db02c520989da5adce55d84410a644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5827acadcb93523ae7fa25204ebcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49fb140af76ff062c908e96e9dab466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69946ed268a024eca1cf522acee6985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0328bf462207065c2e0eaaba1002ef1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aebf62d230cbee1781de6c1d73a7ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若数列
![](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/3c7f1ce82982b8385d78e8e77c8f1e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb701fb5c95b3612e64712d836754860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6ef8ef7af86ebdca4f34a36989a63.png)
(3)若常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e12b644318c5c276a086a82982b8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e909ffa98363a211839d0b1338afbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137510e8bcf483cdb40a0592140a800a.png)
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