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1、一、应用题1设生产某种产品个单位时的成本函数为：（万元）,求：（1）当时的总成本、平均成本和边际成本；（2）当产量为多少时，平均成本最小？解：（1）总成本，平均成本，边际成本 所以，（万元）， （万元）（万元） （2）令 ，得（舍去） 因为是其在定义域内唯一驻点，且该问题确实存在最小值，所以当时，平均成本最小. 2.某厂生产某种产品件时的总成本函数为（元），单位销售价格为（元/件），问产量为多少时可使利润达到最大？最大利润是多少解：成本为：收益为：利润为：，令得，是惟一驻点，利润存在最大值，所以当产量为250个单位时可使利润达到最大，且最大利润为（元）。3投产某产品的固定成本为36(万元)，且
2、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，及产量为多少时，可使平均成本达到最低解：成本函数为：当产量由4百台增至6百台时，总成本的增量为100（万元），令得，（负值舍去）。是惟一驻点，平均成本有最小值，所以当（百台）时可使平均成本达到最低.4已知某产品的边际成本=2（元/件），固定成本为0，边际收益，求：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：边际利润为：令得，。是惟一驻点，最大利润存在，所以当产量为500件时，利润最大。 - 25（元）即利润将减少25元。5已知某产品的边际成本为(万元/百台)，为产量(百台)，固定成本为18
3、(万元)，求最低平均成本. 解：因为总成本函数为 = 当= 0时，C(0) = 18，得 c =18，即 C()= 又平均成本函数为 令 ， 解得= 3 (百台) 该问题确实存在使平均成本最低的产量. 所以当x = 3时，平均成本最低. 最底平均成本为 (万元/百台) 6、已知生产某产品的边际成本为 (万元/百台)，收入函数为（万元），求使利润达到最大时的产量，如果在最大利润的产量的基础上再增加生产台，利润将会发生怎样的变化？解：边际利润为：令得，是惟一驻点，而最大利润存在，所以当产量为3百台时，利润最大。当产量由3百台增加到5百台时，利润改变量为（万元） 即利润将减少4万元。7.设生产某产品
4、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. 8.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 。 二、线性代数计算题1、 设
5、矩阵，求。解：因为 所以，。2、设矩阵A =，I是3阶单位矩阵，求。解：因为，(I-A I ) = 所以=。3设矩阵 A =，B =，计算(AB)-1解：因为AB = (AB I ) = 所以 (AB)-1= 4、设矩阵，求解：求逆矩阵的过程见复习指导P77的4，此处从略 。；所以，。5设矩阵，求解矩阵方程。解： 6.设矩阵，求.解：利用初等行变换得 即 由矩阵乘法得。7求线性方程组的一般解解：因为增广矩阵 所以一般解为 （其中是自由未知量）8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，是自由未知量） 9、当取何值时，齐次线性方程组有非0解？并求一般解。解：因为系数矩阵 所以当
6、= 4时，该线性方程组有无穷多解，且一般解为： （其中是自由未知量）。10、问当取何值时，线性方程组有解，在有解的情况下求方程组的一般解。解：方程组的增广矩阵所以当时，方程组有解；一般解为：（其中是自由未知量）11解：所以，方程组的一般解为：（其中是自由未知量）12求线性方程组.解：将方程组的增广矩阵化为阶梯形 此时齐次方程组化为 得方程组的一般解为其中是自由未知量 13.当为何值时，线性方程组有解，并求一般解。解：所以，当时，有解。一般为：（其中是自由未知量三、微分计算题1设，求解：因为 所以 2计算积分 解： 3设，求解： 4计算积分 解： 5.设，求. 解：由导数运算法则和复合函数求导法
7、则得 6.计算 10分 解：由不定积分的凑微分法得 7.已知，求. 解：由导数运算法则和复合函数求导法则得 8计算. 解：由定积分的分部积分法得四、练习题（1），求解：（2），求解：（3），求解：（4），求解：（5），求解：（6）解：（7）解：（8）解：（9）解：方法1（10）解：（11）解：（12）解：（13）解：（14）解：待添加的隐藏文字内容2五、复习指导1、设，求。解：2、设，求。解：3、设，求。解：4、设，求。解：5、设，求。解：6、设，求。解：7、设，求。解：8、解：原式=9、解：原式=10、解：原式=11、解：原式=12、解：原式=If we dont do that it wi
8、ll 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 general director Roman Babaev says the
9、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 matches played without spectators be
10、cause 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 discrimination can be washed out of fo
11、otball.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 the match tomorrow and I have ask
12、ed 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 Platini, president of European footba
13、lls 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 disappointing news: Mission aborted.The su
14、personic 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 l
15、ower 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. As he cros
16、ses 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, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth becomes the concrete bottom of a sw
17、imming 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 speed of
18、 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 parachute that
19、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 a reser
20、ve 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
