2015年電大?？平?jīng)濟(jì)數(shù)學(xué)基礎(chǔ)12必備復(fù)習(xí)資料小抄

1、;.電大經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ)12復(fù)習(xí)資料小抄一、單項(xiàng)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(duì)中，（ ）中的兩個(gè)函數(shù)相等A.B. C. D. 正確答案：D4下列結(jié)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(diào)函數(shù)(C) 奇函數(shù)的圖形關(guān)于坐標(biāo)原點(diǎn)對(duì)稱(D) 偶函數(shù)的圖形關(guān)于坐標(biāo)原點(diǎn)對(duì)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(dāng)（ ）時(shí)，為無(wú)窮小量A. B. C. D. 正確答案：A7當(dāng)時(shí)，下列變量為無(wú)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(diǎn)處的切線斜率是（ ）(A) (B) (C) (D) 正確答案：D10曲線在點(diǎn)（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(diào)減少的是（ ）(A) (B) (C) (D) 正確答案：B 13下列結(jié)論正確的是（ ）(A) 若，則必是的極值點(diǎn)(B) 使不存在的點(diǎn)，一定是的極值點(diǎn)(C) 是的極值點(diǎn)，且存在，則必有 (D) 是的極值點(diǎn)，則必是的駐點(diǎn)正確答案：C14設(shè)某商品的需求函數(shù)為，則當(dāng)時(shí)，

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(shè)，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(gè)原函數(shù)，則下列等式成立的是( ) A BC D正確答案：B20.設(shè)，是單位矩陣，則（ ）A B C D正確答案：A21.設(shè)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(dāng)條件（ ）成立時(shí)，元線性方程組有解A. B. C. D. 正確答案：D23.設(shè)線性

4、方程組有惟一解，則相應(yīng)的齊次方程組（ ）A無(wú)解 B只有0解 C有非0解 D解不能確定正確答案：B24. 設(shè)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(gè)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(dāng)（）時(shí)線性方程組無(wú)解 (A) (B) (C) (D) 正確答案：A 26. 設(shè)，則（）(A) (B) (C) (D) 正確答案：D27.設(shè)線性方程組有無(wú)窮多解的充分必要條件是（ ）A BC D正確答案：B28設(shè)線性方程組有唯一解，則相應(yīng)的齊次方程組（ ） A只有零解 B有非零解 C無(wú)解 D解不能確定正確答案：A29.設(shè)A為矩陣，B為矩陣，則下列運(yùn)

5、算中（ ）可以進(jìn)行 AAB BABT CA+B DBAT正確答案：A 30. 設(shè)是可逆矩陣，且，則（ ）.A B C D正確答案：C31.設(shè)需求量q對(duì)價(jià)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(wú)窮積分中收斂的是（ ）A. B. C. D. 正確答案：C 33. 設(shè)A為3×4矩陣,B為5×2矩陣,且乘積矩陣有意義,則C為( )矩陣. A.4×2 B. 2×4 C. 3×5 D. 5×3正確答案：B 34. 線性方程組的解的情況是（ ） A.無(wú)解 B.只有0解 C.有唯一解 D.有無(wú)窮多解正確答

6、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：3若函數(shù)，則正確答案：4設(shè)，則函數(shù)的圖形關(guān)于對(duì)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(nèi)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(guò)曲線上的一點(diǎn)（0，1）的切線方程為 .正確答案： 10函數(shù)的駐點(diǎn)是 正確答案：11設(shè)，當(dāng) 時(shí)，是對(duì)稱矩陣正確答案：112已知，當(dāng) 時(shí)，為無(wú)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(shè)線性方程組，且，則時(shí)，方程組有唯一解正確答案：17設(shè)齊次線性方程組

7、，且 = r < n，則其一般解中的自由未知量的個(gè)數(shù)等于 正確答案：n r18線性方程組的增廣矩陣化成階梯形矩陣后為則當(dāng)= 時(shí)，方程組有無(wú)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(diǎn)是 正確答案：21.若，則 正確答案：三、微積分計(jì)算題1已知，求解：由導(dǎo)數(shù)運(yùn)算法則和復(fù)合函數(shù)求導(dǎo)法則得 2設(shè)，求解；3設(shè)，求解：由導(dǎo)數(shù)運(yùn)算法則和復(fù)合函數(shù)求導(dǎo)法則得4設(shè)，求解：由導(dǎo)數(shù)運(yùn)算法則和復(fù)合函數(shù)求導(dǎo)法則得 5 解：= = 6計(jì)算 解 7計(jì)算 解 8計(jì)算 解 9計(jì)算解 = = 10計(jì)算 解 =11 解 = 12 解：=- = 13 = =1 四、代數(shù)計(jì)算題1設(shè)

8、矩陣，求 解：因?yàn)?即 所以 2設(shè)矩陣，是3階單位矩陣，求解：由矩陣減法運(yùn)算得利用初等行變換得 即 3. 設(shè)矩陣 A =，B =，計(jì)算(AB)-1解 因?yàn)锳B = (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?yàn)橄禂?shù)矩陣 所以一般解為（其中，是自由元） 6當(dāng)取何值時(shí)，線性方程組 有解？并求一般解解 因?yàn)樵鰪V矩陣 所以，當(dāng)=0時(shí)，線性方程組有無(wú)窮多解，且一般解為： 是自由未知量五、應(yīng)用題1 投產(chǎn)某產(chǎn)品的固定成本為36（萬(wàn)元），且邊際成本為（萬(wàn)元/百臺(tái)）。試求產(chǎn)量由4百臺(tái)增至6百臺(tái)時(shí)總成本的增量，及產(chǎn)量多少時(shí)，可使平均成本達(dá)到最低？ 當(dāng)產(chǎn)量

9、由4百臺(tái)增至6百臺(tái)時(shí)，總成本的增量為（萬(wàn)元）又令，解得。2已知某產(chǎn)品的邊際成本（萬(wàn)元/百臺(tái)），為產(chǎn)量（百臺(tái)），固定成本為18（萬(wàn)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(tái)）因?yàn)槠骄杀敬嬖谧钚≈?，且駐點(diǎn)唯一，所以，當(dāng)產(chǎn)量為300臺(tái)時(shí)，可使平均成本達(dá)到最低。最低平均成本為 （萬(wàn)元/百臺(tái)）3生產(chǎn)某產(chǎn)品的邊際成本為(萬(wàn)元/百臺(tái))，邊際收入為（萬(wàn)元/百臺(tái)），其中x為產(chǎn)量，問(wèn)(1) 產(chǎn)量為多少時(shí)，利潤(rùn)最大？(2) 從利潤(rùn)最大時(shí)的產(chǎn)量再生產(chǎn)2百臺(tái)，利潤(rùn)有什么變化？ 解 （1）邊際利潤(rùn)函數(shù)為 令 得 （百臺(tái)）又是的唯一駐點(diǎn)，根據(jù)問(wèn)題的實(shí)際意義可知存在最大值，故是的最大值點(diǎn)，即當(dāng)產(chǎn)

10、量為10（百臺(tái)）時(shí)，利潤(rùn)最大 （2）利潤(rùn)函數(shù)即從利潤(rùn)最大時(shí)的產(chǎn)量再生產(chǎn)2百臺(tái)，利潤(rùn)將減少20萬(wàn)元4已知某產(chǎn)品的邊際成本（元/件），固定成本為0，邊際收益。問(wèn)產(chǎn)量為多少時(shí)利潤(rùn)最大？在最大利潤(rùn)產(chǎn)量的基礎(chǔ)上再生產(chǎn)50件，利潤(rùn)將會(huì)發(fā)生什么變化？解：因?yàn)檫呺H利潤(rùn)令，得。是唯一駐點(diǎn)，而該問(wèn)題確實(shí)存在最大值。所以，當(dāng)產(chǎn)量為500件時(shí)，利潤(rùn)最大。當(dāng)產(chǎn)量由500件增加至550件時(shí)，利潤(rùn)改變量為即利潤(rùn)將減少25元。5.設(shè)生產(chǎn)某產(chǎn)品的總成本函數(shù)為 (萬(wàn)元)，其中x為產(chǎn)量，單位：百噸銷售x百噸時(shí)的邊際收入為（萬(wàn)元/百噸），求：(1) 利潤(rùn)最大時(shí)的產(chǎn)量；(2) 在利潤(rùn)最大時(shí)的產(chǎn)量的基礎(chǔ)上再生產(chǎn)1百噸，利潤(rùn)會(huì)發(fā)生什么變化

11、？解：(1) 因?yàn)檫呺H成本為，邊際利潤(rùn) 令，得 由該題實(shí)際意義可知，為利潤(rùn)函數(shù)的極大值點(diǎn)，也是最大值點(diǎn). 因此，當(dāng)產(chǎn)量為7百噸時(shí)利潤(rùn)最大. (2) 當(dāng)產(chǎn)量由7百噸增加至8百噸時(shí)，利潤(rùn)改變量為（萬(wàn)元） 即當(dāng)產(chǎn)量由7百噸增加至8百噸時(shí)，利潤(rùn)將減少1萬(wàn)元。6設(shè)生產(chǎn)某種產(chǎn)品個(gè)單位時(shí)的成本函數(shù)為：（萬(wàn)元）,求：當(dāng)時(shí)的總成本和平均成本； 當(dāng)產(chǎn)量為多少時(shí)，平均成本最??？ 解：因?yàn)榭偝杀尽⑵骄杀竞瓦呺H成本分別為：，所以， 令 ，得（舍去），可以驗(yàn)證是的最小值點(diǎn)，所以當(dāng)時(shí)，平均成本最小。7.某廠每天生產(chǎn)某種產(chǎn)品件的成本函數(shù)為（元）.為使平均成本最低，每天產(chǎn)量應(yīng)為多少？此時(shí)，每件產(chǎn)品平均成本為多少？ 解：因?yàn)?

12、= （） = 令=0，即=0，得=140，= -140（舍去）。=140是在其定義域內(nèi)的唯一駐點(diǎn)，且該問(wèn)題確實(shí)存在最小值。所以=140是平均成本函數(shù)的最小值點(diǎn)，即為使平均成本最低，每天產(chǎn)量應(yīng)為140件. 此時(shí)的平均成本為 =176 （元/件） 8已知某產(chǎn)品的銷售價(jià)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(shè)生產(chǎn)的產(chǎn)品全部售出，求產(chǎn)量為多少時(shí)，利潤(rùn)最大？最大利潤(rùn)是多少？ 解：由已知條件可得收入函數(shù) 利潤(rùn)函數(shù) 求導(dǎo)得 令得，它是唯一的極大值點(diǎn)，因此是最大值點(diǎn) 此時(shí)最大利潤(rùn)為 即產(chǎn)量為300件時(shí)利潤(rùn)最大最大利潤(rùn)是43500元 9. 設(shè)生產(chǎn)某種產(chǎn)品個(gè)單位時(shí)的成本函數(shù)為：（萬(wàn)元

13、）,求：當(dāng)時(shí)的總成本和平均成本；當(dāng)產(chǎn)量為多少時(shí)，平均成本最小？解：因?yàn)榭偝杀尽⑵骄杀竞瓦呺H成本分別為：；，所以，； ， 令 ，得（舍去），可以驗(yàn)證是的最小值點(diǎn)，所以當(dāng)時(shí)，平均成本最小10.設(shè)生產(chǎn)某產(chǎn)品的總成本函數(shù)為 (萬(wàn)元)，其中為產(chǎn)量，單位：百噸銷售百噸時(shí)的邊際收入為（萬(wàn)元/百噸），求：利潤(rùn)最大時(shí)的產(chǎn)量；在利潤(rùn)最大時(shí)的產(chǎn)量的基礎(chǔ)上再生產(chǎn)百噸，利潤(rùn)會(huì)發(fā)生什么變化？解：因?yàn)檫呺H成本為 ，邊際利潤(rùn)令，得可以驗(yàn)證為利潤(rùn)函數(shù)的最大值點(diǎn). 因此，當(dāng)產(chǎn)量為百噸時(shí)利潤(rùn)最大. 當(dāng)產(chǎn)量由百噸增加至百噸時(shí)，利潤(rùn)改變量為 （萬(wàn)元）即利潤(rùn)將減少1萬(wàn)元.11.某廠生產(chǎn)某種產(chǎn)品q件時(shí)的總成本函數(shù)為，單位銷售價(jià)格為，問(wèn)產(chǎn)

14、量為多少時(shí)可使利潤(rùn)最大？最大利潤(rùn)是多少？解：設(shè)產(chǎn)量為q，則收入函數(shù)為因?yàn)檫呺H利潤(rùn)時(shí)，利潤(rùn)最大。則，得產(chǎn)量為250時(shí)可使利潤(rùn)最大最大利潤(rùn)為1230元您好，為你提供優(yōu)秀的畢業(yè)論文參考資料，請(qǐng)您刪除以下內(nèi)容，O(_)O謝謝！A large group of tea merchants on camels and horses from Northwest China's Shaanxi province pass through a stop on the ancient Silk Road, Gansu's Zhangye city during their journey to

15、Kazakhstan, May 5, 2015. The caravan, consisting of more than 100 camels, three horse-drawn carriages and four support vehicles, started the trip from Jingyang county in Shaanxi on Sept 19, 2014. It will pass through Gansu province and Xinjiang Uygur autonomous region, and finally arrive in Almaty,

16、formerly known as Alma-Ata, the largest city in Kazakhstan, and Dungan in Zhambyl province. The trip will cover about 15,000 kilometers and take the caravan more than one year to complete. The caravan is expected to return to Jingyang in March 2016. Then they will come back, carrying specialty produ

17、cts from Kazakhstan A small art troupe founded six decades ago has grown into a household name in the Inner Mongolia autonomous region. In the 1950s, Ulan Muqir Art Troupe was created by nine young musicians, who toured remote villages on horses and performed traditional Mongolian music and dances f

18、or nomadic families. The 54-year-old was born in Tongliao, in eastern Inner Mongolia and joined the troupe in 1975.He says there are 74 branch troupes across Inner Mongolia and actors give around 100 shows every year to local nomadic people. "I can still recall the days when I toured with the t

19、roupe in the early '80s. We sat on the back of pickup trucks for hours. The sky was blue, and we couldn't help but sing the folk songs," Nasun says. The vastness of Inner Mongolia and the lack of entertainment options for people living there, made their lives lonely. "The nomadic p

20、eople were very excited about our visits," Nasun recalls. "We didn't have a formal stage. The audience just sat on the grass. Usually, the performances became a big party with local people joining in." For him, the rewarding part about touring isn't just about sharing art with

21、 nomadic families but also about gaining inspiration for the music and dance. Ulan Muqir literally translates as "red burgeon", and today's performers of the troupe still tour the region's villages and entertain nomadic families, but their fame has spread around the world. On May 1

22、6 and 17, nearly 100 singers and dancers from the troupe performed at Beijing's Poly Theater. Their show, titled Ulan Muqir on the Grassland, depicted the history and development of the art troupe. "Being from the region allowed me to embrace the culture of Inner Mongolia and being a member

23、 of the troupe showed me where I belonged," Nasun, the art troupe's president, who is also a renowned tenor, tells China Daily. During a tour in 1985, he went to a village and met an elderly local man, who told him a story about his friendship with a solider from Shenyang, capital of Northe

24、ast China's Liaoning province, decades ago. The solider gave the old man a handmade saddle when they bid farewell. The story inspired Nasun to write Carved Saddle, a song that later became one of his most popular numbers. Now, every year, Nasun recruits young singers and dancers for the troupe.

25、The troupe has also designed a new repertoire, which is mostly based on the daily lives of Mongolian people, especially the lives of nomadic families, and has combined contemporary musical elements with folk songs of the region. Haimu, a 25-year-old khoomei (a local variant of overtone singing) sing

26、er, joined the troupe three years ago. Along with a six-member band, he performs fast songs and soft ones that he writesall while playing the horse-head fiddle."Although I learned the piano since childhood and grew up listening to various kinds of music, to me, the folk music of Inner Mongolia

27、is the root," he says. "Performing in remote villages is pleasant. I feel at home on the boundless grasslands, and the warm people there make me feel fulfilled." The first round of spring auction season in Beijing ended last week, but it failed to create much spring in the art market.

28、 Although two pieces of Chinese painting fetched more than 100 million yuan, the decline in trading volume and sale rate showed a downturn this year. In the “Grand View: Chinese Painting Highlight” session at China Guardian 2015 spring auctions, Pan Tianshous representative work Eagle, Rock and Flor

29、a hit a record auction price of 279 million yuan, while Li Kerans masterwork Jinggang Mountain fetched 126.5 million yuan, an unexpected high in recent years. However, the trading volume fells to 1.87 billion yuan from 2.22 billion yuan in the same period the year before. The Huangchen 2015 Spring A

30、uctions, which recorded 42.5 million yuan in total sales, experienced the same. The section number went down to 5 from 12 compared to last year. According to expert Shao Jianwu, the art market did not attract much excitement this year due to the booming stock market and the persistent problems of fo

31、rgery and fake deals. The two pieces of Chinese painting notched up high price this spring due to their own value not due to a revival in the market. "The successful transaction of two works with a hammer price of more than 100 million yuan once again confirms that valuable and rare works of hi

32、gh quality always earn the long-lasting high price. Chinese painting and calligraphy is still the pillar of the market. However, the overall sales rate has dropped slightly, which reflects the demand for the ordinary auction goods has weakened,” said the president of China Guardians Hu Yanyan. "

33、;Besides, the entry of new buyers also makes certain changes to the direction of purchasing. In a word, the overall market trend is very unpredictable. Although China Guardian 2015 Spring Auctions has achieved remarkable results, it does not mean that the market has walked out of the predicament. We

34、 still have to wait for the big economic boom to invigorate the art market.” Even so, the hot pursuit of some special items appeared this spring. A special session of China Guardian Spring Auctions titled “Fine GiltBronze Buddhist Images” achieved a great deal with total sales volume of 41.89 millio

35、n yuan and 92 percent sale rate. The 5th Shamar Rinpoche Statue from 16-17th century of Tibet was sold for 5.06 million yuan. The Beijing Chengxuan Auctions featured almost 2,800 items of coins and stamps in three sessions with good sale rate. The Huachen Auctions also set a special session of photo

36、graphs under the condition of large-scale decline of auction sessions. There was a palpable dull thud of disappointment that accompanied the return of the imperial entourage of Zhen Huan to her homeland. It followed a couple years of hushed excitement as Chinese fans were fed tidbits about their pro

37、ud concubine who was supposed to conquer the high ground of the North American market. Zhen Huan is, of course, the title character of The Legend of Zhen Huan, a 2011 television series that swept China off its feet and later took other Asian countries by storm. Two years ago, it was reported that HB

38、O, a premium cable service headquartered in the United States, was going to air it in North America after some modification. Now, a condensed version that provides English subtitles but no dubbing has finally been made available on Netflix for online streaming. This version, highly anticipated as a

39、milestone in China's cultural foray overseas, has been widely panned by its home audience. Retitled Empresses in the Palace, the American version has been shortened from its original 76 episodes at 45 minutes each, to six 90-minute episodes. The quick pacing threw off many native viewers, who ar

40、e accustomed to a more leisurely daytime-soap-style narrative rhythm. (Chinese TV stations would run two or three episodes every day.) I did not finish the full-length version and found the truncated one not difficult to follow. What's lost, I believe, are the interesting setups and pauses that

41、illuminate the Chinese art of storytelling. Much of the plot is still there. It is the flavor that was sacrificed. The American edition uses the framework of the Empress Dowager in her senior years reminiscing at the beginning and the end of each episode, hinting at what's to come and recapping

42、the key points. This device, not used in the original, is culturally understandable but artistically mediocre. What puzzles me is the two new songs for the opening and end credits. They were written in English, but sung by Chinese with an uncomfortable accent. They were obviously designed to appeal

43、to an English-speaking base, but do not jibe with the Chinese dialogue. Speaking of the dialogue, the English translation, picked apart by some Chinese, is too literal for my taste. I can imagine a typical American hit by a flurry of royal ranks, addresses and greetings, even multiple names and titl

44、es for the same person. The first half hour must be a swamp to wade through, very much like my experience of getting through a Tolstoy tome with its endless inflections of names transliterated into lengthy Chinese. I see the choice of verbatim translation as an effort for conveying exotica. It is fa

45、irly competent, with no error that I could detect, but fails to rise above words or capture the essence of the language. A cultural product usually crosses over to a foreign territory first by an emphasis on the commonalities. But whether inside or outside China, the temptation to sell it for the di

46、fferences is just too great. Sure, the sumptuous sets and costumes are a big attraction, but the narrative technique has becomehow shall I put it?a bit anglicized, which is necessary for cultural export. Judging by the responses, this legend, which, contrary to the claim of the English trailer, is t

47、otally fictitious, has departed from China but not yet landed on American shores. I am a big fan of Ralph Waldo Emerson's essay titled Self-Reliance. If you've not yet read it, I strongly encourage you to do so. In this essay, the venerable Emerson talks about eschewing the trappings of soci

48、ety and finding one's own path. He urges the reader to find rectitude and lead a moral life. He professes that, only by being self reliant, as opposed to relying on the government and being dictated to by society, can one begin leading a decent and purposeful life. He avers that such a life is t

49、he only life worth living. I agree with him. This essay was written during a time of social upheaval in America, and it is rather odd that Emerson authored it, as he was a part of the upper crust of society at the time. It just so happened that he looked around him, at the indolence and the wantonne

50、ss of the people in his circle; he wondered how in the world he came to belong there. Indeed his penning and publishing this essay caused his excommunication from high society and also caused him a lot of legal trouble. The legal trouble came as a result of the fact that he was speaking out against the government. I like to reference such texts from time to time a