名校
1 . 已知数列
满足:对任意
,若
,则
,且
,设
,集合
中元素的最小值记为
;集合
,集合
中元素最小值记为
.
(1)对于数列:
,求
,
;
(2)求证:
;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5897fd42e01b077fe8685e7b7a71e278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfbc054e041fa0b53feb9b81a4608347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7aad65e4222bcab9f6ddc94ea495de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f8fdbba79ddbc156bbb300b1b051e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74fd79d9aa9740d095affe36788e01cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a1493a001b60b0e94e342d428caa.png)
(1)对于数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3cf64aad412f59d047c97efa1516175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a1493a001b60b0e94e342d428caa.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aa00523d3ab546ab459d1fff0a6136.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
您最近一年使用:0次
2020-06-13更新
|
479次组卷
|
4卷引用:2020届上海市七宝中学高三三模数学试题
2020届上海市七宝中学高三三模数学试题上海市七宝中学2020届高三下学期模拟数学试题(已下线)卷11-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)(已下线)考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)
2 . 天干地支纪年法源于中国,中国自古便有十天干与十二地支,十天干即甲、乙、丙、丁、戊、己、庚、辛、壬、癸;十二地支即子、丑、寅、卯、辰、巳、午、未、申、酉、戌、亥天干地支纪年法是按顺序以一个天干和一个地支相配,排列起来,天干在前,地支在后,天干由“甲”起,地支由“子”起,例如,第一年为“甲子”,第二年为“乙丑”,第三年为“丙寅”,…,以此类推,排列到“癸酉”后,天于回到“甲”重新开始,即“甲戌”,“乙亥”,然后地支回到“子”重新开始,即“丙子”,以此类推已知1949年为“己丑”年,那么到中华人民共和国成立70年时为( )
A.丙酉年 | B.戊申年 | C.己申年 | D.己亥年 |
您最近一年使用:0次
3 . 天干地支纪年法,源于中国
中国自古便有十天干与十二地支
十天干即甲、乙、丙、丁、戊、己、庚、辛、壬、癸,十二地支即子、丑、寅、卯、辰、巳、午、未、申、酉、戌、亥
天干地支纪年法是按顺序以一个天干和一个地支相配,排列起来,天干在前,地支在后,天干由“甲”起,地支由“子”起,比如说第一年为“甲子”,第二年为“乙丑”,第三年为“丙寅”
依此类推,排列到“癸酉”后,天干回到“甲”重新开始,即“甲戌”“乙亥”,之后地支回到“子”重新开始,即“丙子”
依此类推
已知1949年为“己丑”年,那么到新中国成立80周年时,即2029年为( )
![](https://img.xkw.com/dksih/QBM/2020/5/29/2473201112399872/2473978025721856/STEM/e7c421c06f60410eb6c567c9be4c4f8e.png?resizew=3)
![](https://img.xkw.com/dksih/QBM/2020/5/29/2473201112399872/2473978025721856/STEM/e7c421c06f60410eb6c567c9be4c4f8e.png?resizew=3)
![](https://img.xkw.com/dksih/QBM/2020/5/29/2473201112399872/2473978025721856/STEM/e7c421c06f60410eb6c567c9be4c4f8e.png?resizew=3)
![](https://img.xkw.com/dksih/QBM/2020/5/29/2473201112399872/2473978025721856/STEM/130199c6595e4d54a35e7c17ac37762d.png?resizew=28)
![](https://img.xkw.com/dksih/QBM/2020/5/29/2473201112399872/2473978025721856/STEM/130199c6595e4d54a35e7c17ac37762d.png?resizew=28)
![](https://img.xkw.com/dksih/QBM/2020/5/29/2473201112399872/2473978025721856/STEM/e7c421c06f60410eb6c567c9be4c4f8e.png?resizew=3)
A.己丑年 | B.己酉年 | C.壬巳年 | D.辛未年 |
您最近一年使用:0次
2020-05-30更新
|
167次组卷
|
2卷引用:吉林省长春市实验中学2019-2020学年高二下学期期中考试数学(文科)试卷
解题方法
4 . 在推导很多三角恒等变换公式时,我们可以利用平面向量的有关知识来研究,在一定程度上可以简化推理过程.如我们就可以利用平面向量来推导两角差的余弦公式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
具体过程如下:
如图,在平面直角坐标系
内作单位圆O,以
为始边作角
.它们的终边与单位圆O的交点分别为A,B.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3378e1b0-11ac-4e21-89d7-e7bef545c1e9.png?resizew=334)
则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98717138350884b83b2bc3335ac3262.png)
由向量数量积的坐标表示,有:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437ebce60a1d755209353f0d94462154.png)
设
的夹角为θ,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d77a90728ca9eb4d63b07dbe89e80.png)
另一方面,由图3.1—3(1)可知,
;由图可知,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8e003e58-f755-4f57-ba40-42e3c44c2f0e.png?resizew=348)
.于是
.
所以
,也有
,
所以,对于任意角
有:
(
)
此公式给出了任意角
的正弦、余弦值与其差角
的余弦值之间的关系,称为差角的余弦公式,简记作
.
有了公式
以后,我们只要知道
的值,就可以求得
的值了.
阅读以上材料,利用下图单位圆及相关数据(图中M是AB的中点),采取类似方法(用其他方法解答正确同等给分)解决下列问题:
(1)判断
是否正确?(不需要证明)
(2)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889623d5e61054f38a35aedd644c9ff5.png)
(3)利用以上结论求函数
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
具体过程如下:
如图,在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa404d3ff313b0a28a76a48d7d87234.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3378e1b0-11ac-4e21-89d7-e7bef545c1e9.png?resizew=334)
则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98717138350884b83b2bc3335ac3262.png)
由向量数量积的坐标表示,有:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437ebce60a1d755209353f0d94462154.png)
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538844ce819df320039e394ba92356f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d77a90728ca9eb4d63b07dbe89e80.png)
另一方面,由图3.1—3(1)可知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655ee7e11f540619722504916419e009.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/8e003e58-f755-4f57-ba40-42e3c44c2f0e.png?resizew=348)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18eedcc65589e7529da85a578bd0ecb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e366809cf946d825277ad151abb374a2.png)
所以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a689c643b92f5fafe77fb2c754b0184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
所以,对于任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6276ff5468f5aa9c6eaff479c26cc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e74ca761ffa2566a9851c5ce9ccaaf.png)
此公式给出了任意角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd927b4b5a7875528c1b54aa4bb8b2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e74ca761ffa2566a9851c5ce9ccaaf.png)
有了公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e74ca761ffa2566a9851c5ce9ccaaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1455db71a4123b3317dcfce3e2005e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d521f8d021b20757d7a68107fcef1d.png)
阅读以上材料,利用下图单位圆及相关数据(图中M是AB的中点),采取类似方法(用其他方法解答正确同等给分)解决下列问题:
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90f93aa4ff886e380c9b7c05dbafd08d.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889623d5e61054f38a35aedd644c9ff5.png)
(3)利用以上结论求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1414c4eb3a476aac49f6a35d62b1f7ac.png)
您最近一年使用:0次
2020-05-22更新
|
713次组卷
|
3卷引用:贵阳市普通高中2018-2019学年度高一上学期数学期末质量监测试题
贵阳市普通高中2018-2019学年度高一上学期数学期末质量监测试题贵州省贵阳市2018-2019学年高一(上)期末数学试题(已下线)大题好拿分期中考前必做30题(压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)
5 . 已知数列
满足:对任意的
,若
,则
,且
,设集合
,集合
中元素最小值记为
,集合
中元素最大值记为
.
(1)对于数列:
,写出集合
及
;
(2)求证:
不可能为18;
(3)求
的最大值以及
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a54cba92061cd4470f7fde4ed5c1edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3936ff665accd1cfd1ff790f9dba518e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69836a99a93afdee1fed09226971a83a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f8fdbba79ddbc156bbb300b1b051e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58e9d04712c58c5d5263ce2dc57e6db.png)
(1)对于数列:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f014ca9551d95abc843e906e58c60555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b93b1aca2f6d74a84e04eaef8e211b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03884cbb941b58d23a64e6e9e38ab453.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c342a95c3bc9c6ec834337b12bcf8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58e9d04712c58c5d5263ce2dc57e6db.png)
您最近一年使用:0次
6 . 某企业新研发了一种产品,产品的成本由原料成本及非原料成本组成.每件产品的非原料成本
(元)与生产该产品的数量
(千件)有关,经统计得到如下数据:
根据以上数据,绘制了散点图.观察散点图,两个变量不具有线性相关关系,现考虑用反比例函数模型
和指数函数模型
分别对两个变量的关系进行拟合,已求得:用指数函数模型拟合的回归方程为
,
与
的相关系数
;
,
,
,
,
,
,(其中
);
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/ffb991f0-2be2-48a6-8508-5858eb7072bb.png?resizew=177)
(1)用反比例函数模型求
关于
的回归方程;
(2)用相关系数判断上述两个模型哪一个拟合效果更好(精确到0.01),并用其估计产量为10千件时每件产品的非原料成本.
参考数据:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de698e370cceb9f38400e8f2816e8a46.png)
参考公式:对于一组数据
,
,…,
,其回归直线
的斜率和截距的最小二乘估计分别为:
,
,相关系数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
y | 112 | 61 | 44.5 | 35 | 30.5 | 28 | 25 | 24 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a323be03360218b752b2fad5f22638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfda27fc9b91bd26ce352c83c4e99ef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f371e7ae56154884f247db3a545398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b767339b2214fb3ac31809a5fe01dc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf6237d4f3fd1550002959e3d03d824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/220c0cff560d3b46a8787cc55ea979dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88247c6c2cf1b2d2636c5cb10a02d3ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2500392ea1f21c821b3d412a9ac517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dca10009ebc63cbb45f171445675ed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d9a43db0d4fe4e821769e63445186e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb29d4f30135b151bf1e8843de87082e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc78e3014b36a234b4f9134c904a7f31.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/ffb991f0-2be2-48a6-8508-5858eb7072bb.png?resizew=177)
(1)用反比例函数模型求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)用相关系数判断上述两个模型哪一个拟合效果更好(精确到0.01),并用其估计产量为10千件时每件产品的非原料成本.
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18262127c125047ea24197a752b6320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de698e370cceb9f38400e8f2816e8a46.png)
参考公式:对于一组数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ec1a0fcbbfca5a52a2fb139d0fc5afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/148e67f81a7490d361774a0939949a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be634e851734563d51ca0bdd280d83de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552917a75db1fd1bf0ebaea7bf5e3a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43047c99826b4a779d20951cc3fc46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e38b7c4efeada802316b5d72a07653e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74cf8bbd7a1a79994452907e92fc4780.png)
您最近一年使用:0次
7 . 在我国南宋数学家杨辉所著的《详解九章算法》一书中,用如图所示的三角形(杨辉三角)解释了二项和的乘方规律.右边的数字三角形可以看作当n依次取0,1,2,3,…时
展开式的二项式系数,相邻两斜线间各数的和组成数列
.例:
,
,
,….
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/959e3261-0d5e-4988-8a75-5a06e02faa95.png?resizew=383)
(1)写出数列
的通项公式(结果用组合数表示),无需证明;
(2)猜想
,与
的大小关系,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5abcb3802cf02be93a8c89067bd49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2037221d1ac40cf28e2ef5d60e8edd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0adbf307eef6f3610f342c57ddd275a6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/959e3261-0d5e-4988-8a75-5a06e02faa95.png?resizew=383)
(1)写出数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c587d225f909233b772abf6e6bed9a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ebf2173007b30775097510495febcd.png)
您最近一年使用:0次
解题方法
8 . 衍数列来源于《乾坤谱》中对易传“大衍之数五十”的推论,主要用于解释中国传统文化中的太极衍生原理,数列中的每一项,都代表太极衍生过程中,曾经经历过的两仪数量总和,它是中华传统文化中隐藏着的世界数学史上第一道数列题,该数列从第一项起依次是0,2,4,8,12,18,24,32,40,50…,则该数列第16项为
A.152 | B.134 | C.128 | D.102 |
您最近一年使用:0次
名校
9 . 欧拉公式
(
为虚数单位)是由瑞士著名数学家欧拉发明的,他将指数函数的定义域扩大到复数,建立了三角函数和指数函数的关系,它在复变函数论里占有非常重要的地位,被誉为“数学中的天桥”.根据欧拉公式可知,
表示的复数在复平面中位于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90b4c0b7a519ba3f1d22b8d93c159a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2078fd093b9ab2944b3fd1ff0f08237.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
您最近一年使用:0次
2020-04-30更新
|
799次组卷
|
8卷引用:湖北省仙桃中学2018-2019学年高三上学期期中数学(理)试题
10 . 设等差数列
的首项为0,公差为a,
;等差数列
的首项为0,公差为b,
.由数列
和
构造数表M,与数表
;
记数表M中位于第i行第j列的元素为
,其中
,(i,j=1,2,3,…).
记数表
中位于第i行第j列的元素为
,其中
(
,
,
).如:
,
.
(1)设
,
,请计算
,
,
;
(2)设
,
,试求
,
的表达式(用i,j表示),并证明:对于整数t,若t不属于数表M,则t属于数表
;
(3)设
,
,对于整数t,t不属于数表M,求t的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f0d538cab3daae7d590482989f2a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254fa569dc952c0b78fed34c8a1daf97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
记数表M中位于第i行第j列的元素为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e69701dd0e5844cd75752cd391deef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49128aead2182911b2d154bf8bcd1cf2.png)
记数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc4957c304de68d181441625394edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0227d02cc5bfa2845d30512262a47ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2d219599bb6453e9b8b431a948ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7965f5d265d8b1a5bea91a427dd3a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aabd97c086e3e1a7fcf4a419d0adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef914cefc04d21daa7a7ec165f1d269b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c251824d22684ccb464a910c27f2e204.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86718fa3bd81961f00798692fbf86db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05b891c5f036025713d20bf44c20704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c75905e8c61af58a59edd945b054da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecbb868da9359eec873a17e530b634f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e69701dd0e5844cd75752cd391deef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc4957c304de68d181441625394edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
您最近一年使用:0次