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1、经济数学基础综合练习题解答一、 单项选择题（每小题3分）1、下列函数中，其图像关于轴对称的是（ C ）。A B C D（1奇偶函数定义：）（2奇偶函数运算性质：奇奇=奇；奇偶=非；偶偶=偶；奇奇=偶；奇偶=奇；偶偶=偶）（3奇函数图像关于原点对称；偶函数图像关于轴对称）（4奇偶函数复合性质：奇（奇）=奇；奇（偶）=偶；偶（偶）=偶；偶（奇）=偶）（5常见的奇函数：常见的偶函数：常见的非奇非偶函数：）（A非奇非偶 B奇函数 C偶函数 D非奇非偶）2、下列函数中（ D ）不是奇函数。A； B ； C； D (A奇(常见) B.奇偶=奇 C奇(常见) D非奇非偶)3、下列函数中（ C ）的图像关于坐
2、标原点对称。A B C D （奇函数图像关于原点对称；偶函数图像关于轴对称）(A非奇非偶(常见) B.偶(常见) C偶奇=奇 D. 非奇非偶(常见)4、当 时，是无穷小量的为 （ C ）A B C. D A.； B.;C. ; D. ;5、在指定变化过程中，（ C ）是无穷小量。A BC. D A.；不是无穷小量B.;不是无穷小量C.(有界量与无穷小量的乘积仍然是无穷小量);D,不是无穷小量6、下列极限不正确的是（ B ）。A BC. D A. 正确.（分子最高次幂的指数=分母最高次幂的指数：最高次幂前系数之比）；B. 不正确.C.正确.第一个重要极限; D.正确.第二个重要极限7、设，则（
3、B ）。A ； B ； C ； D 不存在8、设可导，且，则（ C ）。A ； B ； C ； D 不存在9、下列等式中，成立的是（ D ）。A B C D 10、下列等式中，不成立的是（ D ）。A B C D 11、曲线在区间内是（ A ）。A上升且凹 B下降且凹 C上升且凸 D下降且凸12、曲线在区间内是（ B ）。 A上升且凹 B下降且凹 C上升且凸 D下降且凸13、下列无穷积分为收敛的是（D）。A. B.C.D.14、设函数的原函数为，则（ A ）。A ； B； C； D 15、设，则（ B ）。 A B C D 16、设为 上的连续奇函数，且，则由曲线与直线 以及轴围成的平面图形的
4、面积为 ( B )。A B C D17、设A，B均为阶方阵，则下列结论正确的是（ A ）A. B. C. D.若且, 则(A.称为反序性；B.不满足交换律；C.D.不一定成立)18、若，则齐次线性方程组解的情况为（ A ）。A有唯一零解 B有非零解 C无解 D不能确定是否有非零解19、设为阶方阵，为阶单位阵，且，则（ A ）A. ； B. ； C. ； D. 20、设A，B均为阶方阵，则下列结论不正确的是（ A ）A. B. C. D. 若、都可逆,，则 二、 填空题（每小题3分）1、函数的定义域是 2、函数的定义域是 。 3、函数的定义域是 。 4、若函数 在处连续，则= 。 5、若函数 在
5、处连续，则= 2 。 6、曲线上点处的切线方程为 。 7、曲线上横坐标为的点处的切线方程为 。8、已知某种商品的需求函数为，则 。 9、设需求函数，则 。 10、设，则 。 11、= _0_。(因为被积函数为奇函数)12、= _。()13、由连续曲线，与直线,，围成的平面图形面积的定积分表达式为 。 14、设，则_。15、设， ，则 。16、若，则 3 。17、若，则 。18、设，则= 3 。 19、若，则 2 。20、设齐次线性方程组只有零解，则_4_。(齐次线性方程组只有零解(唯一解)三、 微积分学计算题（每小题10分）1、求极限 2、求极限；解：当时， 3、求极限；4、设函数，求； 解：
6、 5、设函数，求；解: 6、设函数，求；解： 11、计算不定积分 ； 原式 12、计算不定积分 ； 原式 13、计算不定积分 原式 14、用抛物线公式计算定积分的近似值，其中的值给出如下表：解：=10.0515、用抛物线公式计算定积分的近似值，其中的值给出如下表：13572568752解：16、用数值积分公式计算定积分的近似值，其中的值给出如下表：待添加的隐藏文字内容3解：四、 线性代数计算题（每小题10分）1、设，求解矩阵方程。2、设，求解矩阵方程。3、设，求解矩阵方程。4、为何值时，线性方程组有解，并求一般解。解： 时方程组有解 一般解为 (为自由未知量) 5、为何值时，线性方程组有解，并
7、求一般解。解： 时方程组有解 一般解为 为自由未知量6、为何值时，线性方程组有解，并求一般解。解： 时方程组有解 一般解为 为自由未知量五、 应用题（每题10分）1、设生产某产品的边际成本为（万元/百吨），固定成本为600万元，求（1）最小平均成本产量；（2）最小平均成本。解: （1） 固定成本为600万元，成本,平均成本,为唯一驻点由于实际问题最小值存在，故10百吨为最小平均成本时的产量。（2）最小平均成本（万元/百吨）2、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：（1）利润最大时的产量；（2）在最大利润产量的基础上再生产百吨，利润
8、会发生什么变化？解：边际成本 边际利润 令可得：（百吨）为最大利润产量 在最大利润产量基础上再生产1百吨，利润将改变（万元） 即利润将减少0.5万元3、 生产某产品的固定成本为80万元，生产q百台该产品的边际成本为（万元/百台），试求：（1）产量为多少时平均成本最小；（2）最小平均成本。解: （1）边际成本=, 固定成本为80万元, 成本= 平均成本 令,得(负的不合题意,舍去) 为唯一驻点 由于实际问题中最小值存在,故20百台为最小平均成本的产量。（2）最小平均成本（万元/百台） Editors note: Judson Jones is a meteorologist, journalis
9、t and photographer. He has freelanced with CNN for four years, covering severe weather from tornadoes to typhoons. Follow him on Twitter: jnjonesjr (CNN) - I will always wonder what it was like to huddle around a shortwave radio and through the crackling static from space hear the faint beeps of the
10、 worlds first satellite - Sputnik. I also missed watching Neil Armstrong step foot on the moon and the first space shuttle take off for the stars. Those events were way before my time.As a kid, I was fascinated with what goes on in the sky, and when NASA pulled the plug on the shuttle program I was
11、heartbroken. Yet the privatized space race has renewed my childhood dreams to reach for the stars.As a meteorologist, Ive still seen many important weather and space events, but right now, if you were sitting next to me, youd hear my foot tapping rapidly under my desk. Im anxious for the next one: a
12、 space capsule hanging from a crane in the New Mexico desert.Its like the set for a George Lucas movie floating to the edge of space.You and I will have the chance to watch a man take a leap into an unimaginable free fall from the edge of space - live.The (lack of) air up there Watch man jump from 9
13、6,000 feet Tuesday, I sat at work glued to the live stream of the Red Bull Stratos Mission. I watched the balloons positioned at different altitudes in the sky to test the winds, knowing that if they would just line up in a vertical straight line we would be go for launch.I feel this mission was cre
14、ated for me because I am also a journalist and a photographer, but above all I live for taking a leap of faith - the feeling of pushing the envelope into uncharted territory.The guy who is going to do this, Felix Baumgartner, must have that same feeling, at a level I will never reach. However, it di
15、d not stop me from feeling his pain when a gust of swirling wind kicked up and twisted the partially filled balloon that would take him to the upper end of our atmosphere. As soon as the 40-acre balloon, with skin no thicker than a dry cleaning bag, scraped the ground I knew it was over.How claustro
16、phobia almost grounded supersonic skydiverWith each twist, you could see the wrinkles of disappointment on the face of the current record holder and capcom (capsule communications), Col. Joe Kittinger. He hung his head low in mission control as he told Baumgartner the disappointing news: Mission abo
17、rted.The supersonic descent could happen as early as Sunday.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 t
18、hrough 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 higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere
19、. As he crosses the boundary layer (called the tropopause), he can expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet (22.7 miles/36.53 kilometers). Here, Fearless Felix will unclip. He will roll back the door.Then, I would assume, he will slowly step out o
20、nto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of 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
21、 into the shallow end.Skydiver preps for the big jumpWhen he jumps, he is expected to reach the speed 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
22、 stop him completely.If he goes too fast or spins out of control, he has a stabilization parachute 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
23、order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). He will have 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
24、 me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).It might not be the moon, but Kittinger free fell from 102,800 feet in 1960 - at the dawn of an infamous space race that captured the hearts of many. Baumgartner will attempt to break that record, a feat t
25、hat boggles the mind. This is one of those monumental moments I will always remember, because there is no way Id miss this.If 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
26、the FAs celebrations - said he wanted to meet Ivory Coast international Toure to discuss his complaint.CSKA general 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 ra
27、cism to be dealt with with fines. You can always find money from somebody to pay them.It is a nonsense to have matches 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 discriminatio
28、n.This is one of the villains we have today in our game. But it is only with harsh sanctions that racism and discrimination 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 1
29、50th anniversary celebrations and will attend 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 has
30、opened disciplinary proceedings against CSKAfor 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 compla
31、int. In a statement the Russian side added: We found no racist insults from fans of CSKA.Baumgartner the disappointing 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 c
32、alm - 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 kil
33、ometers), 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 expect a lot of turbulence.The balloon will slowly drift to the edge of space at 120,000 feet ( Then
34、, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of 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
35、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 speed 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 clos
36、er 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 parachute 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 altit
37、ude 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 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).cause there
