电大经济数学基础12期末复习重点资料考试小抄

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经济数学基础12期末复习资料 一、单项选择题 1.下列函数中为偶函数的是( ).
(A)
     (B)
(C)
    (D) 正确答案:A 2.下列函数中为奇函数的是( ).
(A)
     (B)
(C)
    (D) 正确答案:B 3.下列各函数对中,( )中的两个函数相等. A. B. C. D. 正确答案:D 4.下列结论中正确的是( ). (A) 周期函数都是有界函数 (B) 基本初等函数都是单调函数 (C) 奇函数的图形关于坐标原点对称 (D) 偶函数的图形关于坐标原点对称 正确答案:C 5.下列极限存在的是( ). A. B.
C.   D. 正确答案:A 6.已知,当( )时,为无穷小量. A. B. C. D. 正确答案:A 7.当时,下列变量为无穷小量的是( )
A. B. C. D. 正确答案:
D 8.函数 在x = 0处连续,则k = ( ). A.-2 B.-1 C.1 D.2 正确答案:B 9.曲线在点处的切线斜率是( ). (A)
 (B)  (C)   (D) 正确答案:D  10.曲线在点(0, 1)处的切线斜率为( )。

A. B. C. D. 正确答案:B 11.若,则( ). A.0 B.1 C. 4 D.-4 正确答案:C 12.下列函数在区间上单调减少的是( ). (A) (B) (C) (D) 正确答案:B  13.下列结论正确的是( ). (A) 若,则必是的极值点 (B) 使不存在的点,一定是的极值点 (C) 是的极值点,且存在,则必有 (D) 是的极值点,则必是的驻点 正确答案:C 14.设某商品的需求函数为,则当时,需求弹性为( ). A. B.-3 C.3 D. 正确答案:B 15.若函数,则 ( ). A.-2 B.-1 C.-1.5 D.1.5 正确答案:A 16.函数的连续区间是( ). A. B. C. D. 正确答案:A 17.设,则=( ). A. B. C. D. 正确答案:C 18.下列积分值为0的是( ). A. B. C. D. 正确答案:C 19.若是的一个原函数,则下列等式成立的是( ). A. B. C. D. 正确答案:B 20.设,,是单位矩阵,则=( ). A. B. C. D. 正确答案:A 21.设为同阶方阵,则下列命题正确的是( ).
A.若,则必有或 B.若,则必有,
C.若秩,秩,则秩 D. 正确答案:B 22.当条件( )成立时,元线性方程组有解. A. B. C. D. 正确答案:D 23.设线性方程组有惟一解,则相应的齐次方程组( ). A.无解 B.只有0解 C.有非0解 D.解不能确定 正确答案:B 24. 设线性方程组的增广矩阵为 ,则此线性方程组的一般解中自由未知量的个数为( ). A.1 B.2 C.3 D.4 正确答案:B 25. 若线性方程组的增广矩阵为,则当=( )时线性方程组无解. (A)  (B)   (C) (D) 正确答案:A 26. 设,则( ). (A)  (B)   (C)  (D) 正确答案:D 27.设线性方程组有无穷多解的充分必要条件是( ). A. B. C. D. 正确答案:B 28.设线性方程组有唯一解,则相应的齐次方程组( ). A.只有零解 B.有非零解 C.无解 D.解不能确定 正确答案:A 29.设A为矩阵,B为矩阵,则下列运算中( )可以进行. A.AB B.ABT C.A+B D.BAT 正确答案:A 30. 设是可逆矩阵,且,则( ). A. B. C. D. 正确答案:C 31.设需求量q对价格p的函数为 ,则需求弹性为Ep=( )。

A. B. C. D. 正确答案:D 32.在无穷积分中收敛的是( )
A. B. C. D. 正确答案:C 33. 设A为3×4矩阵,B为5×2矩阵,且乘积矩阵有意义,则C为( )矩阵. A.4×2 B. 2×4 C. 3×5 D. 5×3 正确答案:B 34. 线性方程组的解的情况是( )
A.无解 B.只有0解 C.有唯一解 D.有无穷多解 正确答案:A 二、填空题 1.函数的定义域是   
. 正确答案:
2.函数的定义域是    . 正确答案:
3.若函数,则 . 正确答案:
4.设,则函数的图形关于  对称. 正确答案:y轴 5.已知需求函数为,则收入函数= . 正确答案:
6. 
   . 正确答案:1 7.已知,若在内连续,则 . 正确答案:2 8.曲线在处的切线斜率是  . 正确答案:
9.过曲线上的一点(0,1)的切线方程为 . 正确答案:
10.函数的驻点是   
. 正确答案:
11.设,当   时,是对称矩阵. 正确答案:1 12.已知,当 时,为无穷小量. 正确答案:
13.齐次线性方程组(是)只有零解的充分必要条件是  
 . 正确答案:
14.若,则 = . 正确答案:
15.=     . 正确答案:
16.设线性方程组,且 ,则时,方程组有唯一解. 正确答案:
17.设齐次线性方程组,且 = r < n,则其一般解中的自由未知量的个数等于 . 正确答案:n – r 18.线性方程组的增广矩阵化成阶梯形矩阵后为 则当=   时,方程组有无穷多解. 正确答案:-1 19. 已知齐次线性方程组中为矩阵,则 . 正确答案:3 20.函数的间断点是  
. 正确答案:
21.若,则  
. 正确答案:
三、微积分计算题 1.已知,求. 解:由导数运算法则和复合函数求导法则得 2.设,求. 解;

3.设,求. 解:由导数运算法则和复合函数求导法则得 4.设,求. 解:由导数运算法则和复合函数求导法则得 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:因为   即  所以  2.设矩阵,是3阶单位矩阵,求. 解:由矩阵减法运算得 利用初等行变换得
即   3. 设矩阵 A =,B =,计算(AB)-1. 解 因为AB == (AB I ) = 所以 (AB)-1= 4.解矩阵方程。

解:由,得 所以, 5.求线性方程组的一般解. 解:因为系数矩阵 所以一般解为(其中,是自由元)
6.当取何值时,线性方程组 有解?并求一般解. 解 因为增广矩阵 所以,当=0时,线性方程组有无穷多解,且一般解为:
是自由未知量〕 五、应用题 1. 投产某产品的固定成本为36(万元),且边际成本为(万元/百台)。试求产量由4百台增至6百台时总成本的增量,及产量多少时,可使平均成本达到最低? 当产量由4百台增至6百台时,总成本的增量为 (万元)
又 令,解得。

2.已知某产品的边际成本(万元/百台),为产量(百台),固定成本为18(万元),求最低平均成本. 解:总得成本函数为 平均成本函数为 ,令,解得(百台)
因为平均成本存在最小值,且驻点唯一,所以,当产量为300台时,可使平均成本达到最低。

最低平均成本为 (万元/百台)
3.生产某产品的边际成本为(万元/百台),边际收入为(万元/百台),其中x为产量,问(1) 产量为多少时,利润最大?(2) 从利润最大时的产量再生产2百台,利润有什么变化? 解 (1)边际利润函数为 令 得 (百台)
又是的唯一驻点,根据问题的实际意义可知存在最大值,故是的最大值点,即当产量为10(百台)时,利润最大. (2)利润函数 即从利润最大时的产量再生产2百台,利润将减少20万元. 4.已知某产品的边际成本(元/件),固定成本为0,边际收益。问产量为多少时利润最大?在最大利润产量的基础上再生产50件,利润将会发生什么变化? 解:因为边际利润 令,得。是唯一驻点,而该问题确实存在最大值。所以,当产量为500件时,利润最大。

当产量由500件增加至550件时,利润改变量为 即利润将减少25元。

5.设生产某产品的总成本函数为 (万元),其中x为产量,单位:百吨.销售x百吨时的边际收入为(万元/百吨),求:(1) 利润最大时的产量;
(2) 在利润最大时的产量的基础上再生产1百吨,利润会发生什么变化? 解:(1) 因为边际成本为,边际利润 令,得 由该题实际意义可知,为利润函数的极大值点,也是最大值点. 因此,当产量为7百吨时利润最大. (2) 当产量由7百吨增加至8百吨时,利润改变量为 (万元)
即当产量由7百吨增加至8百吨时,利润将减少1万元。

6.设生产某种产品个单位时的成本函数为:(万元),求:⑴当时的总成本和平均成本;

⑵当产量为多少时,平均成本最小? 解:⑴因为总成本、平均成本和边际成本分别为:
, 所以, , ⑵ 令 ,得(舍去),可以验证是的最小值点,所以当时,平均成本最小。

7.某厂每天生产某种产品件的成本函数为(元).为使平均成本最低,每天产量应为多少?此时,每件产品平均成本为多少? 解:因为 == ()
== 令=0,即=0,得=140,= -140(舍去)。

=140是在其定义域内的唯一驻点,且该问题确实存在最小值。

所以=140是平均成本函数的最小值点,即为使平均成本最低,每天产量应为140件. 此时的平均成本为 ==176 (元/件)
8.已知某产品的销售价格(单位:元/件)是销量(单位:件)的函数,而总成本为(单位:元),假设生产的产品全部售出,求产量为多少时,利润最大?最大利润是多少? 解:由已知条件可得收入函数 利润函数 求导得 令得,它是唯一的极大值点,因此是最大值点. 此时最大利润为 即产量为300件时利润最大.最大利润是43500元. 9. 设生产某种产品个单位时的成本函数为:(万元),求:⑴当时的总成本和平均成本;
⑵当产量为多少时,平均成本最小? 解:⑴因为总成本、平均成本和边际成本分别为:


, 所以,;

, ⑵ 令 ,得(舍去),可以验证是的最小值点,所以当时,平均成本最小. 10.设生产某产品的总成本函数为 (万元),其中为产量,单位:百吨.销售百吨时的边际收入为(万元/百吨),求:⑴利润最大时的产量;
⑵在利润最大时的产量的基础上再生产百吨,利润会发生什么变化? 解:⑴因为边际成本为 ,边际利润 令,得可以验证为利润函数的最大值点. 因此,当产量为百吨时利润最大. ⑵当产量由百吨增加至百吨时,利润改变量为 (万元)
即利润将减少1万元. 11.某厂生产某种产品q件时的总成本函数为 ,单位销售价格为,问产量为多少时可使利润最大?最大利润是多少? 解:设产量为q,则收入函数为 因为边际利润时,利润最大。

则,得 产量为250时可使利润最大 最大利润为1230元 请您删除一下内容,O(∩_∩)O谢谢!!!2015年中央电大期末复习考试小抄大全,电大期末考试必备小抄,电大考试必过小抄请您删除一下内容,O(∩_∩)O谢谢!!!2015年中央电大期末复习考试小抄大全,电大期末考试必备小抄,电大考试必过小抄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 40-year-old 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 instant-messaging 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 6.5 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 top-ranking 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 EE-Media, 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 fu-themed 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 mineral-rich 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 sulfur-containing 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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