中央电大经济数学基础期末复习考试整理题库小抄1

1、 期末复习参考练习题一 单选题1、设，则（ c ）a b c d 2、曲线在点（0，1）处的切线方程为（ a ）。a b c d 3、若，则 b ）a b c d 4、设a，b为同阶可逆矩，则下列等式成立的是（ c ）a b c d 5、线形方程组解的情况是（ d ）a 有无穷多解 b 只有0解 c 有唯一解 d 无解1函数的定义域为（ d ）a b、 c、 d、 2设处的切线方程是（ a ）a b、 c 、 d、 3下列等式中正确的是（ b ）a b、 c、 d、 4、设a为b有意义，则c为（ b ）矩阵。a b c d 5线性方程组解的情况是（ d ）a无解 b、有无穷多解 c 只有0解

2、d 有唯一解1下列结论中 （ d ）是正确的。a 基本初等函数都是单调函数 b 偶函数的图形是关于坐标原点对称c 周期函数都是有界函数 d 奇函数的图形是关于坐标原点 对称2函数（ c ）a -2 b -1 c 1 d 2 3下列等式成立的是（ c ）a、 b、 c、 d 、4、设a，b是同阶方阵，且a是可逆矩阵，满足（ a ）。a、i+b b、 1+b c、 b d、 5、设线性方程组有无穷多解的充分必要条件是（ d ）a、 b、 c、 d、1函数的定义域是（ b ）a b、c d、2若（ a ）a0 b 、 c、 d、3下列函数中，（ d ）是的原函数。a b、 c、 d、4设a是矩阵，b

3、是矩阵，且有意义，则c是（ d ）矩阵。a b、 c、 d、5用消元法解方程组得到的解为（ c ）。a b、 c、 d、1下列各函数对中，（ d ）中的两个函数相等。a、 b、c d、2已知，当（ a ）时，为无穷小量。a、 b、 c、 d、3、（ c ）a、0 b、 c、 d、4、设a是可逆矩阵，且a+ab=i，则=（ c ）a、b b、1+b c、 i+b d、5设线性方程组ax=b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（ b ）a、 1 b、2 c、3 d、41.下列各函数中的两个函数相等的是（ c ）a. b. c. d. 2.下列函数在区间（）上单调增加的是（ c

4、）a. b. c. d. 3. 若是的一个原函数，则下列等式成立的是（ b ）a. b. c. d. 4. 设a，b为同阶可逆矩阵，则下式成立的是（d ）a. b. c. d.5.设线性方程组ax=b有唯一解，则线性方程组ax=o的解的情况是（ a ）a. 只有零解 b.有非零解 c.解不能确定 d.无解二、填空题 6、函数 的定义域是。-5，2 ）7、。08、函数的原函数是。9、设a，b均为n阶矩阵，则等式成立的充分必要条件是。a，b任意10、齐次线性方程组ax=o的系数矩阵为则此方程组的一般解为6、若函数，则。7 、设需求量q对价格p的函数为，则需求弹性为。8。9若则线性方程组ax=b。无

5、解10设，则。6、函数的定义域为。（-3，-2）（-2，3）7、需求量对价格的函数为则需求弹性为。8。09、当时，矩阵是对称矩阵。 310、线性方程组，且，则=时，方程组有无穷多解。-16已知生产某产品的成本函数为则当产量单位时，该产品的平均成本为。3.67、函数的间断点是。8、。29、的秩为。210、若线性方程组 有非0解，则=。-16、若函数则=。7、已知，若内连续，则a=.28、若存在且连续，则=。9、设矩阵，i为单位矩阵，则=. 10、已知齐次线性方程组ax=o中a为3*5矩阵，且该方程组有非0解，则.36 .函数的图型关于对称 坐标原点7.曲线在（处的切线斜率是。 -18. 。 09

6、.两个矩阵a，b既可以相加又可以相乘的充分必要条件是。a，b为同阶矩阵10. 线性方程组ax=b有解的充分必要条件是。 三 计算题11、由方程确定的隐函数，求。解 11设，求。解 11、已知求解 11、 求解、 11、设解 11 .已知，求解：11 求解 11. 求解 11. 求解11. 求解 11. 求解 11 11、 11.由方程确定的隐函数， 求解 11. 由方程确定的隐函数， 求解 11 由方程 确定的隐函数 求 解 当 11 由方程 确定的隐函数 求 解 12、解 12解 12. 解 12、解 =12.计算解： 12、解、12、解、12. 解 12. 解12. 解 12. 解 12.

7、 解 12. 解 12. 解 12. 解 13、设矩阵a=解 因为 所以13设矩阵解 所以 13、设矩阵，计算解： 所以 13、设 求解 所以 13、设矩阵解 13 .已知ax=b，其中，求x解 . 即13.设矩阵 计算解 且 13. 设矩阵， 求逆矩阵 解 且 所以 13.设矩阵 计算 解 13.设矩阵 计算 解 13.解矩阵方程 解 即 13.解矩阵方程 解 即 所以 14.设线性方程组讨论当 为何值时，方程组无解，有唯一解，无穷多解。解 当 方程组无解；当 方程组有唯一解；当 方程组有无穷多解。14求线性方程组的一般解。解因为则一般解为：14、当b为何值时，线性方程组 有解，有解时求一般

8、解。解 所以当b=5是方程组有解，且由得解为14、求线性方程组的一般解。解、一般解为14、设线性方程组 问为何值时方程组有非0解，并求一般解。解 所以当时，方程有非0解，一般解为14、求线性方程组的一般解解 方程组的一般解为：14.当为何值时，线性方程组有解，在有解的情况下求方程组的一般解解 当=3时，方程组有解， 原方程组化为得解 五、应用题15设生产某种产品q单位时的成本函数为：（万元）求：（1）当q=10时的总成本、平均成本和边际成本； （2）当产量q为多少时，平均成本最小？解 （1）总成本 平均成本 边际成本 （2） 令得q=20当产量为20时平均成本最小。15设生产某产品的边际成本为

9、（万元/百台），边际收入为（万元/百台），其中q是产量，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，利润将会发生怎么的变化？解 （1）令，得q=10产量为10百台时利润最大。（2）从利润最大时的产量再生产2百台，利润将减少20万元。15设某工厂生产某产品的固定成本为200（百元），每生产一个单位产品，成本增加5（百元），且已知需求函数，这种产品在市场上是畅销的，（1）试分别列出该产品的总成本函数和总收入函数表达式；（2）求使该产品利润最大的产量及最大利润。解 （1）总成本函数 总收入函数 （2）利润函数为 令 得 产量，即当产量为45单位时利润最大最大利润 15已

10、知某产品的边际成本为（元/件），固定成本为0，边际收入，求：（1）产量为多少时利润最大？（2）在最大利润的基础上再生产50件，利润将会发生什么变化？解：（1）边际利润 令当产量为500是利润最大。（2）当产量由500件增加至550件时，利润改变量为 （元）即利润将减少25元。15、 已知某产品的边际成本为（万元/百台），q为产量（百台），固定成本为18（万元），求（1）该产品的平均成本； （2）最低平均成本。解 （1）成本函数为则平均成本函数为 （2）令 得 最低平均成本为 （万元/百台）15，某厂生产某种产品q千件时的总成本函数为（万元），单位销售价格为（万元/千件），试求（1）产量为多少时

11、可使利润达到最大？（2）最大利润是多少？解（1）由已知得利润函数 从而有令 解，产量为1千件时利润最大。（2）最大利润为（万元）15设生产某种产品q台时的边际成本（元/台），边际收入，试求获得最大利润时的产量。解：边际利润为令 得 当产量为2000时利润最大。15 设某产品的成本函数为（万元）其中q是产量（单位：台），求使平均成本最小的产量，并求最小平均成本是多少？解：平均成本 解得 即当产量为50台时，平均成本最小，最小平均成本为（万元）15。生产某种产品的固定费用是1000万元，每生产1台该品种产品，其成本增加10万元，又知对该产品的需求为（其中q是产销量（单位：台），p是价格（单位：万元

12、），求（1） 使该产品利润最大的产量；（2） 该产品的边际收入。解：（1）设总成本函数为，收入函数为，利润函数为于是得 即生产50台时该种产品能获最大利润。（3） 因为，故边际收入（万元/台）。15 某厂生产一批产品，其固定成本为2000元，每生产一吨产品的成本为60元，对这种产品的市场需求规律为，试求：（1）成本函数，收入函数；（2）产量为多少时利润最大？解：（1）成本函数为因为 ，即所以收入函数为待添加的隐藏文字内容3（2）因为利润函数为 令得即当产量为200吨时利润最大。15 .设某工厂生产的产品的固定成本为50000元，每生产一个单位产品，成本增加100元，又已知需求函数，这种产品在市

13、场上是畅销的，问价格为多少时利润最大？并求最大利润。解：利润函数令得 ，即当价格为300元是利润最大。最大利润为（元）15. 某厂生产某种产品q件时的总成本函数为（元），单位销售价为（元/件），问产量为多少时可以使利润达到最大？最大利润是多少。解：收入函数为 利润函数且 得 即当产量为250件时可使利润最大，且最大利润为（元）15.某厂每天生产某产品q件时的成本为（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：平均成本为令 得 即为使平均成本最低，每天应该生产140件，此时的平均成本为（元/件）15.已知某厂生产q件产品的成本为（万元），要使平均成本最少，应生产多

14、少件产品？解：因为令 得 要使平均成本最小，应生产50件产品。15.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白台增加至6百台时总成本的增量，及产量为多少时，可使平均成本达到最低。解：当产量由4百台增加至6百台时，总成本的增量为（万元）又 得 即产量为6百台时可使平均成本达到最小。15.设生产某产品的总成本函数为（万元），其中q为产量，单位百吨，销售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基础上再生产1百吨，利润会发生什么变化？解：（1）由成本函数得边际成本函数 边际利润 令 得 当产量为7百吨时利润最大。（2）

15、当产量由7百吨增加至8百吨时，利润改变量为（万元）即利润将减少1万元。g an employment tribunal claimemployment tribunals sort out disagreements between employers and employees.you may need to make a claim to an employment tribunal if: you dont agree with the disciplinary action your employer has taken against you your employer dismis

16、ses you and you think that you have been dismissed unfairly.for more information about dismissal and unfair dismissal, seedismissal.you can make a claim to an employment tribunal, even if you haventappealedagainst the disciplinary action your employer has taken against you. however, if you win your

17、case, the tribunal may reduce any compensation awarded to you as a result of your failure to appeal.remember that in most cases you must make an application to an employment tribunal within three months of the date when the event you are complaining about happened. if your application is received af

18、ter this time limit, the tribunal will not usually accept it.if you are worried about how the time limits apply to you, take advice from one of the organisations listed underfurther help.employment tribunals are less formal than some other courts, but it is still a legal process and you will need to

19、 give evidence under an oath or affirmation.most people find making a claim to an employment tribunal challenging. if you are thinking about making a claim to an employment tribunal, you should get help straight away from one of the organisations listed underfurther help.if you are being represented

20、 by a solicitor at the tribunal, they may ask you to sign an agreement where you pay their fee out of your compensation if you win the case. this is known as adamages-based agreement. in england and wales, your solicitor cant charge you more than 35% of your compensation if you win the case.if you a

21、re thinking about signing up for a damages-based agreement, you should make sure youre clear about the terms of the agreement. it might be best to get advice from an experienced adviser, for example, at a citizens advice bureau. to find your nearest cab, including those that give advice by e-mail, c

22、lick onnearest cab.for more information about making a claim to an employment tribunal, seeemployment tribunals.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will att

23、end citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cs

24、kafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added

25、: we found no racist insults from fans of cska.age has reached the end of the beginning of a word. may be guilty in his seems to passing a lot of different life became the appearance of the same day; may be back in the past, to oneself the paranoid weird belief disillusionment, these days, my mind h

26、as been very messy, in my mind constantly. always feel oneself should go to do something, or write something. twenty years of life trajectory deeply shallow, suddenly feel something, do it.一字开头的年龄已经到了尾声。或许是愧疚于自己似乎把转瞬即逝的很多个不同的日子过成了同一天的样子；或许是追溯过去，对自己那些近乎偏执的怪异信念的醒悟，这些天以来，思绪一直很凌乱，在脑海中不断纠缠。总觉得自己自己似乎应该去做点

27、什么，或者写点什么。二十年的人生轨迹深深浅浅，突然就感觉到有些事情，非做不可了。the end of our life, and can meet many things really do?而穷尽我们的一生，又能遇到多少事情是真正地非做不可？during my childhood, think lucky money and new clothes are necessary for new year, but as the advance of the age, will be more and more found that those things are optional; juni

28、or high school, thought to have a crush on just means that the real growth, but over the past three years later, his writing of alumni in peace, suddenly found that isnt really grow up, it seems is not so important; then in high school, think dont want to give vent to out your inner voice can be in

29、the high school children of the feelings in a period, but was eventually infarction when graduation party in the throat, later again stood on the pitch he has sweat profusely, looked at his thrown a basketball hoops, suddenly found himself has already cant remember his appearance.童年时，觉得压岁钱和新衣服是过年必备，

30、但是随着年龄的推进，会越来越发现，那些东西根本就可有可无；初中时，以为要有一场暗恋才意味着真正的成长，但三年过去后，自己心平气和的写同学录的时候，突然就发现是不是真正的成长了，好像并没有那么重要了；然后到了高中，觉得非要吐露出自己的心声才能为高中生涯里的懵懂情愫划上一个句点，但毕业晚会的时候最终还是被梗塞在了咽喉，后来再次站在他曾经挥汗如雨的球场，看着他投过篮球的球框时，突然间发现自己已经想不起他的容颜。originally, this world, can produce a chemical reaction to an event, in addition to resolutely,

31、have to do, and time.原来，这个世界上，对某个事件能产生化学反应的，除了非做不可的坚决，还有，时间。a persons time, your ideas are always special to clear. want, want, line is clear, as if nothing could shake his. also once seemed to be determined to do something, but more often is he backed out at last. dislike his cowardice, finally fou

32、nd that there are a lot of love, there are a lot of miss, like shadow really have been doomed. those who do, just green years oneself give oneself an arm injection, or is a self-righteous spiritual.一个人的时候，自己的想法总是特别地清晰。想要的，不想要的，界限明确，好像没有什么可以撼动自己。也曾经好像已经下定了决心去做某件事，但更多的时候是最后又打起了退堂鼓。嫌恶过自己的怯懦，最终却发现有很多缘分，

33、有很多错过，好像冥冥之中真的已经注定。那些曾经所谓的非做不可，只是青葱年华里自己给自己注射的一支强心剂，或者说，是自以为是的精神寄托罢了。at the moment, the sky is dark, the air is fresh factor after just rained. suddenly thought of blue plaid shirt; those were broken into various shapes of stationery; from the corner at the beginning of deep friendship; have declare

34、d the end of the encounter that havent start planning. those years, those days of do, finally, like youth, will end in our life.此刻，天空是阴暗的，空气里有着刚下过雨之后的清新因子。突然想到那件蓝格子衬衫；那些被折成各种各样形状的信纸；那段从街角深巷伊始的友谊；还有那场还没有开始就宣告了终结的邂逅计划那些年那些天的非做不可，终于和青春一样，都将在我们的人生中谢幕。baumgartner the disappointing news: mission aborted.

35、r plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our d

36、ay-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expec

37、t a lot of turbulence.the supersonic descent could happen as early as sunda.the weathethe balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom o

38、f a swimming pool that he wants to land on, but not too hard. still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he is diving into the shallow end. skydiver preps for the big jumpwhen he jumps, he is expected to reach the s

39、peed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachut

40、e that can be deployed to slow him down. his team hopes its not needed. instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).in order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). he will have

41、a reserve parachute that will open automatically if he loses consciousness at mach speeds.even if everything goes as planned, it wont. baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).ca

42、use thereif we dont do that it will go on and go on. we have to stop it; we need the courage to do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he wanted to meet ivory coast international toure to discuss his complaint.cska genera

43、l director roman babaev says the matter has been exaggerated by the ivorian and the british media.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. you can always find money from somebody to pay them.it is a nonsense to have mat

44、ches played without spectators because it is against the spirit of football and against the visiting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we have today in our game. but it is only with harsh sanctions that racism and discr

45、imination can be washed out of football.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at

46、the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel plat

47、ini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappoin

48、ting news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even hi