电大数学分析专题研究试题及参考答案小抄参考.doc

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1、专业好文档数学分析专题研究试题及参考答案一、填空题（每小题3分，共18分）1集合X中的关系R同时为反身的，对称的，传递的，则该关系R为 .2设E是非空数集，若存在实数，满足1），有；2） ，则称是数集E的下确界。3函数在点的某个邻域内有定义，若 存在，则称函数在点可导。4若是对数函数，则满足函数方程 。5若非零连续函数满足方程，则函数是 函数。6设函数定义在区间上，对于任意的，有 成立，则称在上为下凸函数。二、单项选择题（每小题3分，共18分）1设：，则A（ ）A. = B. C. D. 2已知函数在区间上可导，有，则（ ）。A. 有界 B. 无界 C. 可积 D. 不可积3已知函数与在a,b

2、上可导，且 ，则（ ）。A. B. D. 前三个结论都不对4已知，对于，定义，则在区间0，2上（ ）。A. 连续 B. 不连续 C. 可导 D. 前三个结论都不对5已知是区间上的严格下凸函数，则（ ）。A. B. 最小值唯一 C. D. 最大值唯一6定义在（0，1）上，则在（0，1）上是( )函数A. 有界 B. 无界 C. 周期 D. 偶三、计算题（每小题8分，共32分）1已知，求2求定积分3已知，求。4求四、证明题（每小题8分，共32分）1设数列满足0且，则级数收敛2已知函数在上连续，在内存在二阶导数，且，存在。则至少存在一点，使。3已知，证明4已知函数在上连续非负，且存在一点，使，则。模

3、拟试卷参考答案一、填空题（每小题3分，共18分）1等价关系2，使得345线性6二、单项选择题（每小题3分，共18分）1D 2C 3D 4A 5B 6A三、计算题（每小题8分，共32分）1解： 3解 故 4解 = 四、证明题（每小题8分，共32分）1 证明：因，故存在N，当时，2 即时，有 （4分） 因为级数收敛。 故有。因收敛（7分），故收敛。 2证明：已知f(x)在（a,b）内存在二阶导数，故f(x)在（a,b）内连续，由拉格朗日定理，存在，使得 存在，使得 故存在，使得 3证明：已知在上是上凸函数（2分），故对于有 故 4证明：已知f(x)在a,b上连续且存在使，故存在，使得且当时，（4分

4、），因f(x)非负，故 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 the FAs celebrations - said he wanted to meet Ivory Coast international Toure to discuss his complaint.CSKA gen

5、eral 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

6、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 discrimination.This is one of the villains we have today in our game. But it is only with harsh sanctions that racism and di

7、scrimination 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

8、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 CSKAfor the racist behaviour of their fans duringCitys 2-1 win.Michel P

9、latini, 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 disapp

10、ointing 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 capsu

11、le 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 higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) a

12、nd 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, I would assume, he will slowly step out onto something resembling an Olympic diving platform.Below, the Earth

13、 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 into the shallow end.Skydiver preps for the big jumpWhen he jumps,

14、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 stop him completely.If he goes too fast or spins out of control, he

15、 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 order to deploy this chute successfully, he will have to slow to 172

16、 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