电大复变函数作业卷(四)

专业好文档复变函数作业卷（四）一、 判断题1、数列必收敛。 （）解：因为，故级数发散。2、设，则级数收敛的充要条件是级数与都收敛。 （） 解：由定理4.1.2知是正确的。 3、每个幂级数必在其收敛圆上收敛。 （） 解：收敛圆上的点发散或收敛需要另行判断。 4、若幂级数在点收敛则它必在点收敛。 （） 解：易知级数在处绝对收敛，而其在处也收敛，故其在以为圆心，以为半径的圆内绝对收敛，在圆上但不能判断收敛还是发散。 5、若幂级数在处收敛，则它必在处收。 （） 解：易知级数在以为圆心，以2为半径的圆内各点绝对收敛，在圆内，故收敛。二、填空题。 1、设的收敛域为，则幂级数的收敛域为（）。 2、幂级数的收敛圆中心为（），收敛半径为（2）。 解：，故收敛半径。 3、函数在处所展泰勒级数的半径为（）。 解： 4、设的罗朗级数展开式为，则其收敛圆环域为（C）。 （A） （B） 或 （C） 或（D） 三、计算、证明题。 1、将函数在处展开成泰勒级数，并指出其收敛半径。 解： 故收敛半径为。2、将分别在下列圆环域内展成罗朗级数（1）解：时， 求导得：故（2） 解：时， 3、将在圆环域内展开成罗朗级数。 解： 求导得： 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 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 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 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 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 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 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: 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 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 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, 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 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 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 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 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