2016年电大《数学分析选论》习题全解模拟试题及答案小抄参考

1、PAGE 数学分析续论 模拟试题及答案 单项选择题（） （）设 为单调数列，若存在一收敛子列，这时有 ；不一定收敛；不一定有界； 当且仅当预先假设了为有界数列时，才有成立 （）设在R上为一连续函数，则有 当为开区间时必为开区间；当为闭区间时必为闭区间；当为开区间时必为开区间；以上、都不一定成立 （）设在某去心邻域内可导这时有 若存在，则；若在连续，则A成立；若存在，则；以上、都不一定成立 （）设在上可积，则有 . 在上必定连续；在上至多只有有限个间断点；的间断点不能处处稠密； 在上的连续点必定处处稠密 （）设 为一正项级数这时有 若,则 收敛；若 收敛，则；C若 收敛，则； 以上、都不一定成立

2、二、计算题（） （）试求下列极限：；（）设试求（）试求由曲线 ，直线，以及二坐标轴所围曲边梯形的面积 （）用条件极值方法（Lagrange乘数法）导出从固定点到直线的距离计算公式三、证明题（）（）设在上都连续试证：若，则必存在，满足（）证明在其定义域上为一严格凸函数，并导出不等式：,其中 均为正数( 提示：利用詹森不等式)证明：解 答一、答（）；（）；（）；（）；（）二、解 ； （）1 2 （）所围曲边梯形如右图所示其面积为（）由题意，所求距离的平方（）为的最小值，其中需满足，故此为一条件极小值问题依据 Lagrange 乘数法，设，并令（）由方程组（）可依次解出：最后结果就是所求距离的计算公

3、式注上面的求解过程是由（）求出后直接得到，而不再去算出的值，这是一种目标明确而又简捷的解法三、证（）只需引入辅助函数：易知在上连续，满足，故由介值性定理（或根的存在定理），必存在，满足，即（）的定义域为，在其上满足：，所以为一严格凸函数根据詹森不等式，对任何正数，恒有最后借助函数的严格递增性，便证得不等式（）由于较难直接求出该级数的部分和，因此无法利用部分和的极限来计算级数的和此时可以考虑把该级数的和看作幂级数在处的值，于是问题转为计算 不难知道上述幂级数的收敛域为，经逐项求导得到；这已是一个几何级数，其和为再通过两边求积分，还原得由于这里的，于是求得If we dont do that it

4、 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 general director Roman Babaev says t

5、he 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

6、 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 discrimination can be washed out of

7、 football.The (lack of) air up there HYPERLINK /2012/10/13/opinion/jones-baumgartner-skydive/index.html?hpt=hp_c1Watch 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 m

8、atch 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 HYPERLINK http:/www.bbc.co.uk/sport/0/football/24654499opened disci

9、plinary proceedings against CSKAfor the racist behaviour of their fans during HYPERLINK http:/www.bbc.co.uk/sport/0/football/24615218Citys 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

10、 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 supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting

11、 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

12、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 expect a lot of turbulence.The balloon will slowly drift

13、 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 swimming pool that he wants to land on, but not too hard. Still, hell be traveling fast, so despite the distanc

14、e, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end. HYPERLINK /2010/US/05/21/supersonic.skydive/index.htmlSkydiver 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

15、. 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 can be deployed to slow him down. His team hopes its n

16、ot 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 reserve parachute that will open automatically if he loses

17、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 表4 电子商务网站的维护表项目说明网站基本内容的维护工作及有关数据的备份工作公司新闻的管理及维护向网站

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