最新2015年電大經(jīng)濟數(shù)學基礎12復習資料考試小抄

1、電大經(jīng)濟數(shù)學基礎12復習資料考試小抄一、單項選擇題1下列函數(shù)中為偶函數(shù)的是（ ）(A) (B) (C) (D) 正確答案：A2下列函數(shù)中為奇函數(shù)的是（ ）(A) (B) (C) (D) 正確答案：B3下列各函數(shù)對中，（ ）中的兩個函數(shù)相等A.B. C. D. 正確答案：D4下列結論中正確的是（ ）(A) 周期函數(shù)都是有界函數(shù)(B) 基本初等函數(shù)都是單調函數(shù)(C) 奇函數(shù)的圖形關于坐標原點對稱(D) 偶函數(shù)的圖形關于坐標原點對稱正確答案：C5下列極限存在的是（ ） A B C D正確答案：A6已知，當（ ）時，為無窮小量A. B. C. D. 正確答案：A7當時，下列變量為無窮小量的是（ ）A

2、B C D正確答案： D8函數(shù) 在x = 0處連續(xù)，則k = ()A-2B-1 C1 D2 正確答案：B 9.曲線在點處的切線斜率是（ ）(A) (B) (C) (D) 正確答案：D10曲線在點（0, 1）處的切線斜率為（ ）。A B C D正確答案：B11若，則（ ） A0 B1 C 4 D-4 正確答案：C 12下列函數(shù)在區(qū)間上單調減少的是（ ）(A) (B) (C) (D) 正確答案：B 13下列結論正確的是（ ）(A) 若，則必是的極值點(B) 使不存在的點，一定是的極值點(C) 是的極值點，且存在，則必有 (D) 是的極值點，則必是的駐點正確答案：C14設某商品的需求函數(shù)為，則當時，

3、需求彈性為（ ）A B3 C3 D正確答案：B15若函數(shù)，則( )A-2 B-1 C-1.5 D1.5正確答案：A16函數(shù)的連續(xù)區(qū)間是（ ） A B C D正確答案：A17設，則=（ ） A B C D正確答案：C18下列積分值為0的是（ ） A BC D正確答案：C19若是的一個原函數(shù)，則下列等式成立的是( ) A BC D正確答案：B20.設，是單位矩陣，則（ ）A B C D正確答案：A21.設為同階方陣，則下列命題正確的是（ ）.A.若，則必有或 B.若，則必有,C.若秩,秩，則秩D. 正確答案：B22當條件（ ）成立時，元線性方程組有解A. B. C. D. 正確答案：D23.設線性

4、方程組有惟一解，則相應的齊次方程組（ ）A無解 B只有0解 C有非0解 D解不能確定正確答案：B24. 設線性方程組的增廣矩陣為，則此線性方程組的一般解中自由未知量的個數(shù)為（ ）A1 B2 C3 D4正確答案：B 25. 若線性方程組的增廣矩陣為，則當（）時線性方程組無解 (A) (B) (C) (D) 正確答案：A 26. 設，則（）(A) (B) (C) (D) 正確答案：D27.設線性方程組有無窮多解的充分必要條件是（ ）A BC D正確答案：B28設線性方程組有唯一解，則相應的齊次方程組（ ） A只有零解 B有非零解 C無解 D解不能確定正確答案：A29.設A為矩陣，B為矩陣，則下列運

5、算中（ ）可以進行 AAB BABT CA+B DBAT正確答案：A 30. 設是可逆矩陣，且，則（ ）.A B C D正確答案：C31.設需求量q對價格p的函數(shù)為 ,則需求彈性為Ep=( )。A B. C. D. 正確答案：D32.在無窮積分中收斂的是（ ）A. B. C. D. 正確答案：C 33. 設A為34矩陣,B為52矩陣,且乘積矩陣有意義,則C為( )矩陣. A.42 B. 24 C. 35 D. 53正確答案：B 34. 線性方程組的解的情況是（ ） A.無解 B.只有0解 C.有唯一解 D.有無窮多解正確答案：A二、填空題1函數(shù)的定義域是 正確答案：2函數(shù)的定義域是 .正確答案

6、：3若函數(shù)，則正確答案：4設，則函數(shù)的圖形關于對稱正確答案：y軸5已知需求函數(shù)為，則收入函數(shù)= .正確答案：6 正確答案：1 7已知，若在內連續(xù)，則 正確答案：28曲線在處的切線斜率是正確答案：9過曲線上的一點（0，1）的切線方程為 .正確答案： 10函數(shù)的駐點是 正確答案：11設，當 時，是對稱矩陣正確答案：112已知，當 時，為無窮小量正確答案：13齊次線性方程組（是）只有零解的充分必要條件是 正確答案：14若，則= .正確答案：15= 正確答案：16設線性方程組，且，則時，方程組有唯一解正確答案：17設齊次線性方程組，且 = r n，則其一般解中的自由未知量的個數(shù)等于 正確答案：n r1

7、8線性方程組的增廣矩陣化成階梯形矩陣后為則當= 時，方程組有無窮多解.正確答案：-119. 已知齊次線性方程組中為矩陣，則 正確答案：320.函數(shù)的間斷點是 正確答案：21.若，則 正確答案：三、微積分計算題1已知，求解：由導數(shù)運算法則和復合函數(shù)求導法則得 2設，求解；3設，求解：由導數(shù)運算法則和復合函數(shù)求導法則得4設，求解：由導數(shù)運算法則和復合函數(shù)求導法則得 5 解：= = 6計算 解 7計算 解 8計算 解 9計算解 = = 10計算 解 =11 解 = 12 解：=- = 13 = =1 四、代數(shù)計算題1設矩陣，求 解：因為 即 所以 2設矩陣，是3階單位矩陣，求解：由矩陣減法運算得利用

8、初等行變換得 即 3. 設矩陣 A =，B =，計算(AB)-1解 因為AB = (AB I ) = 所以 (AB)-1= 4.解矩陣方程。解：由，得所以，5求線性方程組的一般解 解：因為系數(shù)矩陣 所以一般解為（其中，是自由元） 6當取何值時，線性方程組 有解？并求一般解解 因為增廣矩陣 所以，當=0時，線性方程組有無窮多解，且一般解為： 是自由未知量五、應用題1 投產某產品的固定成本為36（萬元），且邊際成本為（萬元/百臺）。試求產量由4百臺增至6百臺時總成本的增量，及產量多少時，可使平均成本達到最低？ 當產量由4百臺增至6百臺時，總成本的增量為（萬元）又令，解得。2已知某產品的邊際成本（萬

9、元/百臺），為產量（百臺），固定成本為18（萬元），求最低平均成本解：總得成本函數(shù)為平均成本函數(shù)為 ，令，解得（百臺）因為平均成本存在最小值，且駐點唯一，所以，當產量為300臺時，可使平均成本達到最低。最低平均成本為 （萬元/百臺）3生產某產品的邊際成本為(萬元/百臺)，邊際收入為（萬元/百臺），其中x為產量，問(1) 產量為多少時，利潤最大？(2) 從利潤最大時的產量再生產2百臺，利潤有什么變化？ 解 （1）邊際利潤函數(shù)為 令 得 （百臺）又是的唯一駐點，根據(jù)問題的實際意義可知存在最大值，故是的最大值點，即當產量為10（百臺）時，利潤最大 （2）利潤函數(shù)即從利潤最大時的產量再生產2百臺，利潤

10、將減少20萬元4已知某產品的邊際成本（元/件），固定成本為0，邊際收益。問產量為多少時利潤最大？在最大利潤產量的基礎上再生產50件，利潤將會發(fā)生什么變化？解：因為邊際利潤令，得。是唯一駐點，而該問題確實存在最大值。所以，當產量為500件時，利潤最大。當產量由500件增加至550件時，利潤改變量為即利潤將減少25元。5.設生產某產品的總成本函數(shù)為 (萬元)，其中x為產量，單位：百噸銷售x百噸時的邊際收入為（萬元/百噸），求：(1) 利潤最大時的產量；(2) 在利潤最大時的產量的基礎上再生產1百噸，利潤會發(fā)生什么變化？解：(1) 因為邊際成本為，邊際利潤 令，得 由該題實際意義可知，為利潤函數(shù)的極

11、大值點，也是最大值點. 因此，當產量為7百噸時利潤最大. (2) 當產量由7百噸增加至8百噸時，利潤改變量為（萬元） 即當產量由7百噸增加至8百噸時，利潤將減少1萬元。6設生產某種產品個單位時的成本函數(shù)為：（萬元）,求：當時的總成本和平均成本； 當產量為多少時，平均成本最?。?解：因為總成本、平均成本和邊際成本分別為：，所以， 令 ，得（舍去），可以驗證是的最小值點，所以當時，平均成本最小。7.某廠每天生產某種產品件的成本函數(shù)為（元）.為使平均成本最低，每天產量應為多少？此時，每件產品平均成本為多少？ 解：因為 = （） = 令=0，即=0，得=140，= -140（舍去）。=140是在其定義

12、域內的唯一駐點，且該問題確實存在最小值。所以=140是平均成本函數(shù)的最小值點，即為使平均成本最低，每天產量應為140件. 此時的平均成本為 =176 （元/件） 8已知某產品的銷售價格（單位：元件）是銷量（單位：件）的函數(shù)，而總成本為（單位：元），假設生產的產品全部售出，求產量為多少時，利潤最大？最大利潤是多少？ 解：由已知條件可得收入函數(shù) 利潤函數(shù) 求導得 令得，它是唯一的極大值點，因此是最大值點 此時最大利潤為 即產量為300件時利潤最大最大利潤是43500元 9. 設生產某種產品個單位時的成本函數(shù)為：（萬元）,求：當時的總成本和平均成本；當產量為多少時，平均成本最??？解：因為總成本、平均

13、成本和邊際成本分別為：；，所以，； ， 令 ，得（舍去），可以驗證是的最小值點，所以當時，平均成本最小10.設生產某產品的總成本函數(shù)為 (萬元)，其中為產量，單位：百噸銷售百噸時的邊際收入為（萬元/百噸），求：利潤最大時的產量；在利潤最大時的產量的基礎上再生產百噸，利潤會發(fā)生什么變化？解：因為邊際成本為 ，邊際利潤令，得可以驗證為利潤函數(shù)的最大值點. 因此，當產量為百噸時利潤最大. 當產量由百噸增加至百噸時，利潤改變量為 （萬元）即利潤將減少1萬元.11.某廠生產某種產品q件時的總成本函數(shù)為，單位銷售價格為，問產量為多少時可使利潤最大？最大利潤是多少？解：設產量為q，則收入函數(shù)為因為邊際利潤時

14、，利潤最大。則，得產量為250時可使利潤最大最大利潤為1230元請您務必刪除一下內容，O(_)O萬分謝謝！2015年中央電大期末復習考試小抄大全，電大期末考試必備小抄，電大考試必過小抄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 govern

15、ment 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, b

16、y 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

17、 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 t

18、he 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 an

19、nounced. 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

20、 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,

21、 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 ove

22、r 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.

23、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

24、 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

25、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 tw

26、in 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

27、 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

28、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 illustrati

29、on 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 mixe

30、d 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

31、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.

32、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 be

33、en 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 Japa

34、n. 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 com

35、puterized 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 h

36、aven, 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 offer

37、s 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

38、 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 student

39、s 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

40、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 r

41、easons 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 propo

42、sed 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 eco

43、nomic 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