1、復變函數作業卷（四）一、 判斷題1、數列必收斂。 （）解：因為，故級數發散。2、設，則級數收斂的充要條件是級數與都收斂。 （） 解：由定理4.1.2知是正確的。 3、每個冪級數必在其收斂圓上收斂。 （） 解：收斂圓上的點發散或收斂需要另行判斷。 4、若冪級數在點收斂則它必在點收斂。 （） 解：易知級數在處絕對收斂，而其在處也收斂，故其在以為圓心，以為半徑的圓內絕對收斂，在圓上但不能判斷收斂還是發散。 5、若冪級數在處收斂，則它必在處收。 （） 解：易知級數在以為圓心，以2為半徑的圓內各點絕對收斂，在圓內，故收斂。二、填空題。 1、設的收斂域為，則冪級數的收斂域為（）。 2、冪級數的收斂圓中心為

2、（），收斂半徑為（2）。 解：，故收斂半徑。 3、函數在處所展泰勒級數的半徑為（）。 解： 4、設的羅朗級數展開式為，則其收斂圓環域為（c）。 （a） （b） 或 （c） 或（d） 三、計算、證明題。 1、將函數在處展開成泰勒級數，并指出其收斂半徑。 解： 故收斂半徑為。2、將分別在下列圓環域內展成羅朗級數（1）解：時， 求導得：故（2） 解：時， 3、將在圓環域內展開成羅朗級數。 解： 求導得： 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

3、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,

4、 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.

5、 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 h

6、ead 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

7、 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

8、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 impo

9、rtant 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 weath

10、er 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 turb

11、ulence.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 tr

12、aveling 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

13、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,

14、 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 speed