济数学基础12期末复资料
单项选择题
1．列函数中偶函数（ ）．
(A) (B)
(C) (D)
正确答案：A
2．列函数中奇函数（ ）．
(A) (B)
(C) (D)
正确答案：B
3．列函数中（ ）中两函数相等．
A
B
C
D
正确答案：D
4．列结中正确（ ）．
(A) 周期函数界函数
(B) 基初等函数单调函数
(C) 奇函数图形关坐标原点称
(D) 偶函数图形关坐标原点称
正确答案：C
5．列极限存（ ）．
A． B．
C． D．
正确答案：A
6．已知（ ）时穷量．
A B C D
正确答案：A
7．时列变量穷量（ ）
A． B． C． D．
正确答案： D
8．函数 x 0处连续k ( )．
A．2 B．1 C．1 D．2
正确答案：B
9曲线点处切线斜率（ ）．
(A) (B) (C) (D)
正确答案：D
10．曲线点（0 1）处切线斜率（ ）
A． B． C． D．
正确答案：B
11．（ ）．
A．0 B．1 C． 4 D．4
正确答案：C
12．列函数区间单调减少（ ）．
(A) (B) (C) (D)
正确答案：B
13．列结正确（ ）．
(A) 必极值点
(B) 存点定极值点
(C) 极值点存必
(D) 极值点必驻点
正确答案：C
14．设某商品需求函数时需求弹性（ ）．
A． B．－3 C．3 D．
正确答案：B
15．函数
( )．
A．2 B．1 C．15 D．15
正确答案：A
16．函数连续区间（ ）．
A． B．
C． D．
正确答案：A
17．设（ ）．
A． B． C． D．
正确答案：C
18．列积分值0（ ）．
A． B．
C． D．
正确答案：C
19．原函数列等式成立( )．
A．
B．
C．
D．
正确答案：B
20设单位矩阵＝（ ）．
A． B．
C． D．
正确答案：A
21设阶方阵列命题正确（ ）
A必
B必
C秩秩秩
D
正确答案：B
22．条件（ ）成立时元线性方程组解．
A B C D
正确答案：D
23设线性方程组惟解相应齐次方程组（ ）．
A．解 B．0解 C．非0解 D．解确定
正确答案：B
24 设线性方程组增广矩阵
线性方程组般解中未知量数（ ）．
A．1 B．2 C．3 D．4
正确答案：B
25 线性方程组增广矩阵＝（ ）时线性方程组解．
(A) (B) (C) (D)
正确答案：A
26 设（ ）．
(A) (B) (C) (D)
正确答案：D
27设线性方程组穷解充分必条件（ ）．
A． B．
C． D．
正确答案：B
28．设线性方程组唯解相应齐次方程组（ ）．
A．零解 B．非零解 C．解 D．解确定
正确答案：A
29设A矩阵B矩阵列运算中（ ）进行．
A．AB B．ABT C．A+B D．BAT
正确答案：A
30 设逆矩阵（ ）
A． B． C． D．
正确答案：C
31设需求量q价格p函数 需求弹性Ep( )
A． B
C D
正确答案：D
32穷积分中收敛（ ）
A B
C D
正确答案：C
33 设A3×4矩阵B5×2矩阵积矩阵意义C( )矩阵
A4×2 B 2×4 C 3×5 D 5×3
正确答案：B
34 线性方程组解情况（ ）
A解 B0解 C唯解 D穷解
正确答案：A
二填空题
1．函数定义域 ．
正确答案：
2．函数定义域
正确答案：
3．函数 ．
正确答案：
4．设函数图形关 称．
正确答案：y轴
5．已知需求函数收入函数
正确答案：
6． ．
正确答案：1
7．已知连续 ．
正确答案：2
8．曲线处切线斜率 ．
正确答案：
9．曲线点（01）切线方程
正确答案：
10．函数驻点 ．
正确答案：
11．设 时称矩阵．
正确答案：1
12．已知 时穷量．
正确答案：
13．齐次线性方程组（）零解充分必条件 ．
正确答案：
14．
正确答案：
15． ．
正确答案：
16．设线性方程组
时方程组唯解．
正确答案：
17．设齐次线性方程组 r < n般解中未知量数等 ．
正确答案：n – r
18．线性方程组增广矩阵化成阶梯形矩阵
时方程组穷解
正确答案：1
19 已知齐次线性方程组中矩阵 ．
正确答案：3
20函数间断点 ．
正确答案：
21
．
正确答案：
三微积分计算题
1．已知求．
解：导数运算法复合函数求导法
2．设求．
解
3．设求．
解：导数运算法复合函数求导法
4．设求．
解：导数运算法复合函数求导法
5．
解：
6．计算
解
7．计算
解
8．计算
解
9．计算
解
10．计算
解
11．
解
12．
解：
13．
＝1
四代数计算题
1．设矩阵求．
解：
2．设矩阵3阶单位矩阵求．
解：矩阵减法运算
利初等行变换
3 设矩阵 A B 计算(AB)1．
解 AB
(AB I )
(AB)1
4解矩阵方程
解：
5．求线性方程组般解．
解：系数矩阵
般解（中元） 6．取值时线性方程组
解？求般解．
解 增广矩阵
0时线性方程组穷解般解：
未知量〕
五应题
1． 投产某产品固定成36（万元）边际成（万元百台）试求产量4百台增6百台时总成增量产量少时均成达低？
产量4百台增6百台时总成增量
（万元）
令解
2．已知某产品边际成（万元百台）产量（百台）固定成18（万元）求低均成．
解：总成函数
均成函数
令解（百台）
均成存值驻点唯产量300台时均成达低
低均成 （万元百台）
3．生产某产品边际成(万元百台)边际收入（万元百台）中x产量问(1) 产量少时利润？(2) 利润时产量生产2百台利润什变化？
解 （1）边际利润函数
令 （百台）
唯驻点根问题实际意义知存值值点产量10（百台）时利润．
（2）利润函数
利润时产量生产2百台利润减少20万元．
4．已知某产品边际成（元件）固定成0边际收益问产量少时利润？利润产量基础生产50件利润会发生什变化？
解：边际利润
令唯驻点该问题确实存值产量500件时利润
产量500件增加550件时利润改变量
利润减少25元
5设生产某产品总成函数 (万元)中x产量单位：百吨．销售x百吨时边际收入（万元百吨）求：(1) 利润时产量(2) 利润时产量基础生产1百吨利润会发生什变化？
解：(1) 边际成边际利润
令
该题实际意义知利润函数极值点值点 产量7百吨时利润
(2) 产量7百吨增加8百吨时利润改变量
（万元）
产量7百吨增加8百吨时利润减少1万元
6．设生产某种产品单位时成函数：（万元）求：⑴时总成均成 ⑵产量少时均成？
解：⑴总成均成边际成分：
⑵
令 （舍）验证值点时均成
7某厂天生产某种产品件成函数（元）均成低天产量应少？时件产品均成少？
解： （）
令00140 140（舍）
140定义域唯驻点该问题确实存值
140均成函数值点均成低天产量应140件
时均成
176 （元件）
8．已知某产品销售价格（单位：元／件）销量（单位：件）函数总成（单位：元）假设生产产品全部售出求产量少时利润？利润少？
解：已知条件收入函数
利润函数
求导
令唯极值点值点．
时利润
产量300件时利润．利润43500元．
9 设生产某种产品单位时成函数：（万元）求：⑴时总成均成⑵产量少时均成？
解：⑴总成均成边际成分：
⑵
令 （舍）验证值点时均成．
10设生产某产品总成函数 (万元)中产量单位：百吨．销售百吨时边际收入（万元百吨）求：⑴利润时产量⑵利润时产量基础生产百吨利润会发生什变化？
解：⑴边际成 边际利润
令验证利润函数值点 产量百吨时利润
⑵产量百吨增加百吨时利润改变量
（万元）
利润减少1万元
11某厂生产某种产品q件时总成函数
单位销售价格问产量少时利润？利润少？
解：设产量q收入函数
边际利润时利润
产量250时利润
利润1230元
请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄The battle for young viewers CCTV is embracing Internet culture and working with independent producers on TV shows to woo audiences under 35 Han Bing bin reports After charming audiences with his warm smile for 14 years China Central Television host Li Jiaming recently found himself targeted by a group of young netizens unhappy with his style The complaints came after Li hosted the premiere of Rising Star on Oct 31 It is a singing competition show that originated in Israel Many young netizens found his hosting style slow and boring and mocked it as CCTV evening gala style They even initiated an online campaign to replace him The 40yearold host＇s reaction to the criticism was surprising During the second episode he jokingly called himself the slow Jiaming and acted much younger talking faster and louder It＇s like selling a product When the customers file a complaint you must change says Li In the Internet age you get feedback very quickly These young people are so cute When you＇re willing to change for them they will quickly like you back In order to win more young viewers CCTV is relying on programs such as Rising Star to embrace Internet culture In Rising Star a studio audience and fans watching on television vote for their favorite singers in real time using the instantmessaging app WeChat Rising Star was designed to be a live broadcast but the Chinese version isn＇t because of policy reasons Still WeChat votes by viewers at home are still a major factor in determining which contestants advance to the next round In the show＇s latest episode more than 65 million votes were cast via WeChat Now the competition among entertainment shows is very fierce Audiences have more diverse needs CCTV needs to embrace an open attitude interact with young audiences and blend with the Internet says Lyu Yitao director of CCTV＇s entertainment channel The producer of Rising Star Enlight Media says the program will have a phenomenal effect given CCTV＇s audience base nationwide But it comes with a challenge says Zhang Hang chief producer of the program and CEO of Enlight Media＇s TV business Unlike topranking provincial satellite channels such as Hunan TV which have a large base of young fans thanks to a series of phenomenally popular entertainment and reality shows CCTV productions are usually more conservative and serious and thus have a much older audience base If we were to run this program on Hunan we may attract twice as many viewers says Zhang But since we didn＇t make it there we now have to make the best out of the given conditions And it means we have to make certain compromises When the current season of Rising Star ends Zhang says his company will conduct an overall evaluation of the program and make adjustments for future seasons Although audience ratings haven＇t lived up to Zhang＇s expectations he says the program has already helped CCTV attract more young people According to Enlight Media the number of people ages 15 to 35 who watched the first episode of Rising Star was 76 percent higher than the usual audience for CCTV entertainment productions In order to attract young audiences CCTV has been working with independent production companies As one of CCTV＇s closest partners Enlight Media has produced several entertainment and reality shows for the company＇s channels including the Chinese version of The Biggest Loser on CCTV＇s business channel and an original teenager talent show Shaonian Zhongguo－qiang (Strong Young Chinese) on CCTV1 This year CCTV also licensed EEMedia the producer of the popular Super Girl talent shows to produce the talk show Hi 2014 hosted by Taiwan pop star Harlem Yu and one of China＇s most popular TV stars Xie Na The show is geared toward younger audiences Canxing Productions which rose to fame with the success of its Voice of China series on Zhejiang TV also produced two talent shows for CCTV One is an original production called Songs of China which ended up as one of CCTV＇s most watched programs of 2014 The State Administration of Press Publication Radio Film and Television announced earlier this year that starting in 2015 only one music talent show can be aired nationwide during prime time each season and there can be only one program based on foreign formats each year However domestic media report that such policies don＇t apply to CCTV meaning it will become a highly desired platform by production companies Wang Changtian CEO of Enlight Media confirmed to the Shanghai Securities News that its programs scheduled to air on CCTV next year which include at least two reality shows won＇t be affected A kung futhemed reality show produced by Canxing is also reportedly scheduled to run on CCTV next year CCTV is very active The level of its acceptance of new ideas is even beyond my imagination says Zhang Hang Our cooperation with CCTV will surely continue When winter comes nothing is more relaxing than a hot spring bath For thousands of years natural mineralrich hot spring baths have also been used to relieve health ailments The water found in natural hot springs contains a variety of different minerals and the most common one is sulfur It has a rotten egg smell but is excellent for skin The sulfurcontaining water might be just what the doctor ordered when it comes to relieving pain stress itchy skin arthritis and more Hot springs resorts are thriving as biting cold winter arrives Here we take a look at some of the best natural hot springs China has to offer
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单项选择题
1．列函数中偶函数（ ）．
(A) (B)
(C) (D)
正确答案：A
2．列函数中奇函数（ ）．
(A) (B)
(C) (D)
正确答案：B
3．列函数中（ ）中两函数相等．
A
B
C
D
正确答案：D
4．列结中正确（ ）．
(A) 周期函数界函数
(B) 基初等函数单调函数
(C) 奇函数图形关坐标原点称
(D) 偶函数图形关坐标原点称
正确答案：C
5．列极限存（ ）．
A． B．
C． D．
正确答案：A
6．已知（ ）时穷量．
A B C D
正确答案：A
7．时列变量穷量（ ）
A． B． C． D．
正确答案： D
8．函数 x 0处连续k ( )．
A．2 B．1 C．1 D．2
正确答案：B
9曲线点处切线斜率（ ）．
(A) (B) (C) (D)
正确答案：D
10．曲线点（0 1）处切线斜率（ ）
A． B． C． D．
正确答案：B
11．（ ）．
A．0 B．1 C． 4 D．4
正确答案：C
12．列函数区间单调减少（ ）．
(A) (B) (C) (D)
正确答案：B
13．列结正确（ ）．
(A) 必极值点
(B) 存点定极值点
(C) 极值点存必
(D) 极值点必驻点
正确答案：C
14．设某商品需求函数时需求弹性（ ）．
A． B．－3 C．3 D．
正确答案：B
15．函数
( )．
A．2 B．1 C．15 D．15
正确答案：A
16．函数连续区间（ ）．
A． B．
C． D．
正确答案：A
17．设（ ）．
A． B． C． D．
正确答案：C
18．列积分值0（ ）．
A． B．
C． D．
正确答案：C
19．原函数列等式成立( )．
A．
B．
C．
D．
正确答案：B
20设单位矩阵＝（ ）．
A． B．
C． D．
正确答案：A
21设阶方阵列命题正确（ ）
A必
B必
C秩秩秩
D
正确答案：B
22．条件（ ）成立时元线性方程组解．
A B C D
正确答案：D
23设线性方程组惟解相应齐次方程组（ ）．
A．解 B．0解 C．非0解 D．解确定
正确答案：B
24 设线性方程组增广矩阵
线性方程组般解中未知量数（ ）．
A．1 B．2 C．3 D．4
正确答案：B
25 线性方程组增广矩阵＝（ ）时线性方程组解．
(A) (B) (C) (D)
正确答案：A
26 设（ ）．
(A) (B) (C) (D)
正确答案：D
27设线性方程组穷解充分必条件（ ）．
A． B．
C． D．
正确答案：B
28．设线性方程组唯解相应齐次方程组（ ）．
A．零解 B．非零解 C．解 D．解确定
正确答案：A
29设A矩阵B矩阵列运算中（ ）进行．
A．AB B．ABT C．A+B D．BAT
正确答案：A
30 设逆矩阵（ ）
A． B． C． D．
正确答案：C
31设需求量q价格p函数 需求弹性Ep( )
A． B
C D
正确答案：D
32穷积分中收敛（ ）
A B
C D
正确答案：C
33 设A3×4矩阵B5×2矩阵积矩阵意义C( )矩阵
A4×2 B 2×4 C 3×5 D 5×3
正确答案：B
34 线性方程组解情况（ ）
A解 B0解 C唯解 D穷解
正确答案：A
二填空题
1．函数定义域 ．
正确答案：
2．函数定义域
正确答案：
3．函数 ．
正确答案：
4．设函数图形关 称．
正确答案：y轴
5．已知需求函数收入函数
正确答案：
6． ．
正确答案：1
7．已知连续 ．
正确答案：2
8．曲线处切线斜率 ．
正确答案：
9．曲线点（01）切线方程
正确答案：
10．函数驻点 ．
正确答案：
11．设 时称矩阵．
正确答案：1
12．已知 时穷量．
正确答案：
13．齐次线性方程组（）零解充分必条件 ．
正确答案：
14．
正确答案：
15． ．
正确答案：
16．设线性方程组
时方程组唯解．
正确答案：
17．设齐次线性方程组 r < n般解中未知量数等 ．
正确答案：n – r
18．线性方程组增广矩阵化成阶梯形矩阵
时方程组穷解
正确答案：1
19 已知齐次线性方程组中矩阵 ．
正确答案：3
20函数间断点 ．
正确答案：
21
．
正确答案：
三微积分计算题
1．已知求．
解：导数运算法复合函数求导法
2．设求．
解
3．设求．
解：导数运算法复合函数求导法
4．设求．
解：导数运算法复合函数求导法
5．
解：
6．计算
解
7．计算
解
8．计算
解
9．计算
解
10．计算
解
11．
解
12．
解：
13．
＝1
四代数计算题
1．设矩阵求．
解：
2．设矩阵3阶单位矩阵求．
解：矩阵减法运算
利初等行变换
3 设矩阵 A B 计算(AB)1．
解 AB
(AB I )
(AB)1
4解矩阵方程
解：
5．求线性方程组般解．
解：系数矩阵
般解（中元） 6．取值时线性方程组
解？求般解．
解 增广矩阵
0时线性方程组穷解般解：
未知量〕
五应题
1． 投产某产品固定成36（万元）边际成（万元百台）试求产量4百台增6百台时总成增量产量少时均成达低？
产量4百台增6百台时总成增量
（万元）
令解
2．已知某产品边际成（万元百台）产量（百台）固定成18（万元）求低均成．
解：总成函数
均成函数
令解（百台）
均成存值驻点唯产量300台时均成达低
低均成 （万元百台）
3．生产某产品边际成(万元百台)边际收入（万元百台）中x产量问(1) 产量少时利润？(2) 利润时产量生产2百台利润什变化？
解 （1）边际利润函数
令 （百台）
唯驻点根问题实际意义知存值值点产量10（百台）时利润．
（2）利润函数
利润时产量生产2百台利润减少20万元．
4．已知某产品边际成（元件）固定成0边际收益问产量少时利润？利润产量基础生产50件利润会发生什变化？
解：边际利润
令唯驻点该问题确实存值产量500件时利润
产量500件增加550件时利润改变量
利润减少25元
5设生产某产品总成函数 (万元)中x产量单位：百吨．销售x百吨时边际收入（万元百吨）求：(1) 利润时产量(2) 利润时产量基础生产1百吨利润会发生什变化？
解：(1) 边际成边际利润
令
该题实际意义知利润函数极值点值点 产量7百吨时利润
(2) 产量7百吨增加8百吨时利润改变量
（万元）
产量7百吨增加8百吨时利润减少1万元
6．设生产某种产品单位时成函数：（万元）求：⑴时总成均成 ⑵产量少时均成？
解：⑴总成均成边际成分：
⑵
令 （舍）验证值点时均成
7某厂天生产某种产品件成函数（元）均成低天产量应少？时件产品均成少？
解： （）
令00140 140（舍）
140定义域唯驻点该问题确实存值
140均成函数值点均成低天产量应140件
时均成
176 （元件）
8．已知某产品销售价格（单位：元／件）销量（单位：件）函数总成（单位：元）假设生产产品全部售出求产量少时利润？利润少？
解：已知条件收入函数
利润函数
求导
令唯极值点值点．
时利润
产量300件时利润．利润43500元．
9 设生产某种产品单位时成函数：（万元）求：⑴时总成均成⑵产量少时均成？
解：⑴总成均成边际成分：
⑵
令 （舍）验证值点时均成．
10设生产某产品总成函数 (万元)中产量单位：百吨．销售百吨时边际收入（万元百吨）求：⑴利润时产量⑵利润时产量基础生产百吨利润会发生什变化？
解：⑴边际成 边际利润
令验证利润函数值点 产量百吨时利润
⑵产量百吨增加百吨时利润改变量
（万元）
利润减少1万元
11某厂生产某种产品q件时总成函数
单位销售价格问产量少时利润？利润少？
解：设产量q收入函数
边际利润时利润
产量250时利润
利润1230元
请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄请您删容O(∩_∩)O谢谢2015年中央电期末复考试抄全电期末考试必备抄电考试必抄The battle for young viewers CCTV is embracing Internet culture and working with independent producers on TV shows to woo audiences under 35 Han Bing bin reports After charming audiences with his warm smile for 14 years China Central Television host Li Jiaming recently found himself targeted by a group of young netizens unhappy with his style The complaints came after Li hosted the premiere of Rising Star on Oct 31 It is a singing competition show that originated in Israel Many young netizens found his hosting style slow and boring and mocked it as CCTV evening gala style They even initiated an online campaign to replace him The 40yearold host＇s reaction to the criticism was surprising During the second episode he jokingly called himself the slow Jiaming and acted much younger talking faster and louder It＇s like selling a product When the customers file a complaint you must change says Li In the Internet age you get feedback very quickly These young people are so cute When you＇re willing to change for them they will quickly like you back In order to win more young viewers CCTV is relying on programs such as Rising Star to embrace Internet culture In Rising Star a studio audience and fans watching on television vote for their favorite singers in real time using the instantmessaging app WeChat Rising Star was designed to be a live broadcast but the Chinese version isn＇t because of policy reasons Still WeChat votes by viewers at home are still a major factor in determining which contestants advance to the next round In the show＇s latest episode more than 65 million votes were cast via WeChat Now the competition among entertainment shows is very fierce Audiences have more diverse needs CCTV needs to embrace an open attitude interact with young audiences and blend with the Internet says Lyu Yitao director of CCTV＇s entertainment channel The producer of Rising Star Enlight Media says the program will have a phenomenal effect given CCTV＇s audience base nationwide But it comes with a challenge says Zhang Hang chief producer of the program and CEO of Enlight Media＇s TV business Unlike topranking provincial satellite channels such as Hunan TV which have a large base of young fans thanks to a series of phenomenally popular entertainment and reality shows CCTV productions are usually more conservative and serious and thus have a much older audience base If we were to run this program on Hunan we may attract twice as many viewers says Zhang But since we didn＇t make it there we now have to make the best out of the given conditions And it means we have to make certain compromises When the current season of Rising Star ends Zhang says his company will conduct an overall evaluation of the program and make adjustments for future seasons Although audience ratings haven＇t lived up to Zhang＇s expectations he says the program has already helped CCTV attract more young people According to Enlight Media the number of people ages 15 to 35 who watched the first episode of Rising Star was 76 percent higher than the usual audience for CCTV entertainment productions In order to attract young audiences CCTV has been working with independent production companies As one of CCTV＇s closest partners Enlight Media has produced several entertainment and reality shows for the company＇s channels including the Chinese version of The Biggest Loser on CCTV＇s business channel and an original teenager talent show Shaonian Zhongguo－qiang (Strong Young Chinese) on CCTV1 This year CCTV also licensed EEMedia the producer of the popular Super Girl talent shows to produce the talk show Hi 2014 hosted by Taiwan pop star Harlem Yu and one of China＇s most popular TV stars Xie Na The show is geared toward younger audiences Canxing Productions which rose to fame with the success of its Voice of China series on Zhejiang TV also produced two talent shows for CCTV One is an original production called Songs of China which ended up as one of CCTV＇s most watched programs of 2014 The State Administration of Press Publication Radio Film and Television announced earlier this year that starting in 2015 only one music talent show can be aired nationwide during prime time each season and there can be only one program based on foreign formats each year However domestic media report that such policies don＇t apply to CCTV meaning it will become a highly desired platform by production companies Wang Changtian CEO of Enlight Media confirmed to the Shanghai Securities News that its programs scheduled to air on CCTV next year which include at least two reality shows won＇t be affected A kung futhemed reality show produced by Canxing is also reportedly scheduled to run on CCTV next year CCTV is very active The level of its acceptance of new ideas is even beyond my imagination says Zhang Hang Our cooperation with CCTV will surely continue When winter comes nothing is more relaxing than a hot spring bath For thousands of years natural mineralrich hot spring baths have also been used to relieve health ailments The water found in natural hot springs contains a variety of different minerals and the most common one is sulfur It has a rotten egg smell but is excellent for skin The sulfurcontaining water might be just what the doctor ordered when it comes to relieving pain stress itchy skin arthritis and more Hot springs resorts are thriving as biting cold winter arrives Here we take a look at some of the best natural hot springs China has to offer
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