电大专科经济数学基础12期末复习资料考试小抄【最新完整版.doc

电大经济数学基础12期末复习资料考试小抄【最新完整版】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：A2下列函数中为奇函数的是（ ）(A) (B) (C) (D) 正确答案：B3下列各函数对中，（ ）中的两个函数相等A.B. C. D. 正确答案：D4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：C5下列极限存在的是（ ） A B C D正确答案：A6已知，当（ ）时，为无穷小量A. B. C. D. 正确答案：A7当时，下列变量为无穷小量的是（ ）A B C D正确答案： D8函数 在x = 0处连续，则k = ()A-2B-1 C1 D2 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：D10曲线在点（0, 1）处的切线斜率为（ ）。A B C D正确答案：B11若，则（ ） A0 B1 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：C14设某商品的需求函数为，则当时，需求弹性为（ ）A B3 C3 D正确答案：B15若函数，则( )A-2 B-1 C-1.5 D1.5正确答案：A16函数的连续区间是（ ） A B C D正确答案：A17设，则=（ ） A B C D正确答案：C18下列积分值为0的是（ ） A BC D正确答案：C19若是的一个原函数，则下列等式成立的是( ) A BC D正确答案：B20.设，是单位矩阵，则（ ）A B C D正确答案：A21.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：B22当条件（ ）成立时，元线性方程组有解A. B. C. D. 正确答案：D23.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：B24. 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（ ）A1 B2 C3 D4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：D27.设线性方程组有无穷多解的充分必要条件是（ ）A BC D正确答案：B28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：A29.设A为矩阵，B为矩阵，则下列运算中（ ）可以进行 AAB BABT CA+B DBAT正确答案：A 30. 设是可逆矩阵，且，则（ ）.A B C D正确答案：C31.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：D32.在无穷积分中收敛的是（ ）A. B. C. D. 正确答案：C 33. 设A为34矩阵,B为52矩阵,且乘积矩阵有意义,则C为( )矩阵. A.42 B. 24 C. 35 D. 53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：28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：112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 r18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：-119. 已知齐次线性方程组中为矩阵，则 正确答案：320.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：当时的总成本和平均成本； 当产量为多少时，平均成本最小？ 解：因为总成本、平均成本和边际成本分别为：，所以， 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：当时的总成本和平均成本；当产量为多少时，平均成本最小？解：因为总成本、平均成本和边际成本分别为：；，所以，； ， 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：利润最大时的产量；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：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. 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元请您务必删除一下内容，O(_)O万分谢谢！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Indonesia has emerged as a top vacation destination for Chinese this summer, along with Thailands Phuket island and the Maldives archipelago. Encouraged by growth in Chinese travelers to Indonesia, the government in Jakarta has recently relaxed its visa policy. Since June 10, Chinese tourists can enter Indonesia through nine appointed locations, including the Soekarno Hatta International Airport in Jakarta, the Ngurah Rai International Airport in Bali and the Kuala Namu International Airport in Medan, by just getting their passports stamped on arrival. Officially, it is called the free-visa scheme. The new policy also means Chinese tourists can save $35 on visa fees, which will likely make trips to Indonesia more alluring. While such an arrangement allows Chinese visitors to stay up to 30 days for the purpose of traveling, those seeking extensions will need to get paid visas from that countrys missions inBeijing,Shanghai,GuangzhouorHong Kong, according to an official at the Indonesia embassy in Beijing. Santo Darmosumarto, head of the embassys information, social and cultural section, says the new policy is aimed at strengthening people-to-people contacts between the two countries. Dai Yu, marketing director of Ctrip, a major Chinese online travel agency, says: Weve seen a nearly 50 percent growth over the previous month in the number of Chinese tourists to Bali since the policy was announced. During his trip to China in March, Indonesian President Joko Widodo proposed that his country and China aim to increase two-way visits to a maximum of 10 million people in the next few years. The Indonesian government has set their sights on greeting 2 million Chinese tourists by the end of this year, according to the official. The Indonesian government hopes that Indonesian nationals would also be given preferential treatment while visiting China, says Darmosumarto. In 2013, the number of Chinese tourists who visited Indonesia stood around 807,000. Last year, it increased to 959,000, he adds. Bali remains the most popular site among Chinese tourists. In February, more than 92,200 Chinese tourists made trips to Bali, ranking first among overseas visitors, the Bali Times reported. Last year, the island witnessed more than 586,000 arrivals from China, an increase of 51 percent over 2013. Bali isnt just for sightseeing, but also for weddings, honeymoons, golf and many outdoor activities, says Fan Wenqing, a marketing executive at Garuda, Indonesias national airliner. Garuda offers three nonstop flights between Beijing and Bali, and four each week between Beijing and Jakarta. There are daily flights from Guangzhou, inGuangdongprovince, and Shanghai to Jakarta as well. It takes from six to eight hours on a nonstop flight to reach Indonesia from China. Indonesia is home to more than 17,000 islands. Tourists can tour Yogyakarta to see Prambanam and Borobudur, two historical and religious sites, and explore the local handicraft markets. The base of a volcano, Bandung, which is also known as the Paris of Java, is ideal for adventure-seekers. Many ecotourism destinations, such as Toba Lake in Sumatra, Tanjung Puting National Park in Kalimantan and Bunaken in Manado, are places the embassy official recommends for tourists. Indonesia boasts world-class surfing facilities along the shores of Sumatra down to Nusa Tenggara Islands. Recently, Lombok, a sister island east of Bali has gotten so much attention from Chinese travelers that some travel agencies are offering twin packages for Bali and Lombok. The best time to visit Bali is from May to October, when it doesntrainmuch and the weather is cool. At press time, a weeklong package from Shanghai or Guangzhou to Bali was a little more than 3,000 yuan ($480) on Ctrips website. Chinese tourists have taken a shine to rafting in Ubud, sightseeing in Tanah Lot, and surfing and diving in Nusa Lembongan, says Dai. Civet coffee, essential oil and woodcarvings are among the most popular products for Chinese tourists in Indonesia, she says. Indonesian food is also something that visitors shouldnt miss. Local cuisines feature many spices, including peppers and cloves, and coconut pulp. Fried rice, dirty duck and roast suckling pig are recommended. Childrens illustration books first appeared in the 1600s in Europe. Their passage to China, however, took much longer, roughly 300 years. In China, childrens illustration books have a history of just 100 years and their development can be divided into four stages. From early 1900s to mid 1900s, a large number of books and magazines with illustrations appeared with the fast development of the modern publishing industry. The illustrationarts at that time were a mixed genre of Chinese traditionalpaintings and the westernstyle, and most of the stories originate from the fundamental changes that China experienced after the collapse of Qing Dynasty (1644-1911), the warlord struggles and the war against the Japanese invasion. The second stage was from mid 1900s to late 1970s, when the cultural revolution (1966-76) ended. The fast development of some special publishing houses for children gave birth to a large number of illustration-story books, which made a good use of folk art techniques, such as wood board carving, frescoes, and ink and wash painting, etc. Many of the popular stories are from Chinese history and wars after 1900s. The third stage is from early 1980s to late 1990s, a golden period for the development of childrens illustration books. The reform and opening-up brought in new concepts and ideas from the West to China, a country that had been closed to the West for nearly three decades. Fast development of economy, society and culture provided the writers and painters with a lot of inspiration to create new literature works and draw illustrations. China also imported large amounts of childrens illustration books from the West and Japan. Many young parents in China have a strong nostalgia about childrens illustration books they read in the 1980s and 1990s. This is also the last era in Chinas artistic innovation before the advent of the Internet period. The fourth stage is featured with the spread of the Internet and the other computerized means of art innovation. The hand-drawn childrens illustration books are gradually replaced by cartoons drawn and copied by software and machines, and shown on tablets, computers, television and smart phones, instead of books. Hainan Tropical Wildlife Park and Botanical Garden is natures haven, with no less than 4,000 rare birds and animals representing 200 species. With tropical forest covering over 90 percent of its area, the garden offers beautiful views of a wide range of tropical plants, flowers and fruit trees. The scenic spot about 25 kilometers from the center of Haikou offers a drive-thru safari tour where you can get up close with elephants, lions and bears. The Safari on Foot area features walking trails where visitors can see the rest of the animals, including hippos and monkeys, and feed them for a small fee. Visitors also can see what happens when you breed a lion and a tiger. Two unique attractions are rare hybrids: a liger, the offspring of a mallion and a female tiger and a tigon, which is created by a female lion and a male tiger. As ateaching center of the National Popular Science Education program, the park also serves as a second classroom for students to learn about wildlife and plants. Since it was established in 1995, it has received more than one million student visitors. At a crucial moment when pessimism has brought the Greek crisis to such a head that the country is closer to a default on its debt repayments than ever, Li offered a spark of enthusiasm to restart the stalled talks by calling on Greece and its creditors to reach a last-minute deal that will allow Greece to remain in the eurozone. Given the escalation of the countrys crisis over the weekend sent a shock wave through the global stock markets on Monday, there are ample reasons to worry about the uncertainties surrounding the events in Greece and the effect a default would have on Europe, relations between China and the EU, global financial stability and the nascent global economic recovery. Greece has announced that it will hold a referendum on a bailout plan proposed last week by the countrys creditors. In response, Greeces eurozone partners have refused to extend the countrys bailout program and the European Central Bank capped its emergency support for the countrys banks. A real danger now looms of Greece exiting the euro, which might derail the global economic recovery and damage the long-term viability of the euro as a currency. However, such a tragedy is neither certain nor unavoidable. The EU should shoulder its responsibility to prevent the Greek crisis from overshadowing the fragile global recovery. As a major customer and supplier of the 28-nation EU, and a responsible long-term holder of Eurobonds, Chinas confidence in and commitment to a strong eurozone offers EU leaders the necessary support to look at the Greek crisis from a broader and longer perspective. When Li said that China will not onl