電大【數(shù)學分析專題研究】試題模擬試題及參考答案小抄參考

1、專業(yè)好文檔一、填空題（每小題3分，共18分）1集合x中的關(guān)系r同時為反身的，對稱的，傳遞的，則該關(guān)系r為 .2設(shè)e是非空數(shù)集，若存在實數(shù)，滿足1），有；2） ，則稱是數(shù)集e的下確界.3函數(shù)在點的某個鄰域內(nèi)有定義，若 存在，則稱函數(shù)在點可導。4若是對數(shù)函數(shù)，則滿足函數(shù)方程 。5若非零連續(xù)函數(shù)滿足方程，則函數(shù)是 函數(shù)。6設(shè)函數(shù)定義在區(qū)間上，對于任意的，有 成立，則稱在上為下凸函數(shù)。二.單項選擇題（每題3分） 1.設(shè)：,則a（ ）. a. = ; b.; c.; d. 2已知函數(shù)在區(qū)間上可導，有，則（ ）。a. 有界 b. 無界 c. 可積 d. 不可積3已知函數(shù)與在a,b上可導，且 ，則（ ）。a

2、. b. d. 前三個結(jié)論都不對4已知，對于，定義，則在區(qū)間0，2上（ ）。 a. 連續(xù) b. 不連續(xù) c. 可導 d. 前三個結(jié)論都不對5已知是區(qū)間上的嚴格下凸函數(shù),則（ ）a. b. 最小值唯一 c. d. 最大值唯一6定義在（0,1）上,則在（0,1）上是( )函數(shù). a. 有界b. 無界c. 周期d. 偶三、計算題（每小題8分，共32分）1已知，求 2求定積分3已知，求。 4求四、證明題（每題8分）1設(shè)數(shù)列滿足0且，則級數(shù)收斂2已知函數(shù)在上連續(xù)，在內(nèi)存在二階導數(shù)，且，存在。則至少存在一點，使。3已知，證明4已知函數(shù)在上連續(xù)非負，且存在一點，使，則。參考答案:一.1.等價關(guān)系 2.,使得

3、 3. 4. 5.線性 6. 二. 1.d, 2.c, 3.d, 4.a, 5.b, 6.a三.1解： 3.解 故 4解= .四.證明題 1 證明：因，故存在n，當時，2 即時,有,因為級數(shù)收斂. 故有.因收斂,故收斂 2證明：已知f(x)在（a,b）內(nèi)存在二階導數(shù)，故f(x)在（a,b）內(nèi)連續(xù)，由拉格朗日定理，存在，使得存在，使得 故存在，使得 3證明：已知在上是上凸函數(shù)（2分），故對于有 故 4證明：已知f(x)在a,b上連續(xù)且存在使，故存在，使得且當時，（4分），因f(x)非負，故 if we dont do that it will go on and go on. we have t

4、o 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 b

5、y 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 spiri

6、t 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 t

7、here 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 tol

8、d 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

9、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

10、 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

11、(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 (calle

12、d 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

13、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)

14、- 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 d

15、own. 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 consciousne