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电大经济数学基础12复习资料小抄一、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元您好，为你提供优秀的毕业论文参考资料，请您删除以下内容，O(_)O谢谢！A large group of tea merchants on camels and horses from Northwest Chinas Shaanxi province pass through a stop on the ancient Silk Road, Gansus Zhangye city during their journey to 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, 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 products 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 for 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 troupe in the early 80s. We sat on the back of pickup trucks for hours. The sky was blue, and we couldnt 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 people were very excited about our visits, Nasun recalls. We didnt 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 isnt just about sharing art with nomadic families but also about gaining inspiration for the music and dance. Ulan Muqir literally translates as red burgeon, and todays performers of the troupe still tour the regions villages and entertain nomadic families, but their fame has spread around the world. On May 16 and 17, nearly 100 singers and dancers from the troupe performed at Beijings 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 of the troupe showed me where I belonged, Nasun, the art troupes 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 Northeast Chinas 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. 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) singer, 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 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. 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 Flora 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 Auctions, 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 forgery 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 high 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. 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 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 million 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 photographs 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 proud 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 HBO, 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 milestone in Chinas 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 are 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. Whats lost, I believe, are the interesting setups and pauses that 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 whats to come and recapping 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 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 titles 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 fairly 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 differences 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 totally fictitious, has departed from China but not yet landed on American shores. I am a big fan of Ralph Waldo Emersons essay titled Self-Reliance. If youve not yet read it, I strongly encourage you to do so. In this essay, the venerable Emerson talks about eschewing the trappings of society and finding ones 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 the 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 wantonness 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 as an example both of the fact that history does repeat itself and that this world is not so big that what applies to one society does not in any way touch another society. On a much smaller scale,Emersons essay affects me very deeply. Not as an urging to become self reliant Im nothing if not that! In his text he expounds on the idea that one must give their life a purpose. And that is the true topic of this entry. These last four years have been so easy: teach for a grand total of six hours a week, and the rest of my time is mine. Since Ive been here I have been tasked with nothing more challenging than learning my students names and figuring out what to do with them for the brief time each week that I stand in front of them. I do not consider the challenges of learning to live here part of a purposeful life. I consider those issues existential in nature. One of the problems with my life in America was that I felt it had no purpose. I went to work every day and even did what I could to make my colleagues work lives easier, but I simply could not digest the fact that that was my sole purpose in life. With no family to support, I was the sole beneficiary of my employment: the paycheck, the benefits, the incentives and the rewards were mine alone. Not much of a purpose in being self-serving, is there? While I was a student, I felt I was leading a purposeful life. Learning new things, broadening my horizons, expanding my life experiences all gave my life a zip and drive that I had not felt since being in survival mode when my kids were small. After graduating college I felt oddly deflated but by then, China was on my horizon.
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