電大數(shù)學(xué)分析(Ⅱ)試題與參考答案小抄參考

1、專業(yè)好文檔數(shù)學(xué)分析（2）期末試題課程名稱 數(shù)學(xué)分析（）適 用 時 間 試卷類別 1 適用專業(yè)、年級、班 應(yīng)用、信息專業(yè) 一、單項選擇題（每小題3分，3618分）1、 下列級數(shù)中條件收斂的是（ ）a b c d 2、 若是內(nèi)以為周期的按段光滑的函數(shù), 則的傅里葉（fourier）級數(shù)在它的間斷點處 （ ）a收斂于 b收斂于 c 發(fā)散 d可能收斂也可能發(fā)散3、函數(shù)在上可積的必要條件是（ ）a有界 b連續(xù) c單調(diào) d存在原函數(shù)4、設(shè)的一個原函數(shù)為，則（ ）a b c d 5、已知反常積分收斂于1，則（ ）a b c d 6、收斂，則（ ）a b c 為任意實數(shù) d 二、填空題（每小題3分，3618分

2、）1、已知冪級數(shù)在處條件收斂，則它的收斂半徑為 2、若數(shù)項級數(shù)的第個部分和，則其通項 ，和 3、曲線與直線，及軸所圍成的曲邊梯形面積為 4、已知由定積分的換元積分法可得，則 ， 5、數(shù)集的聚點為 6、函數(shù)的麥克勞林（maclaurin）展開式為 65 三、計算題（每小題6分，6530分）1、 2、3、 4、5、四、解答題（第1小題6分，第2、3 小題各8分，共22分）1、討論函數(shù)項級數(shù)在區(qū)間上的一致收斂性2、求冪級數(shù)的收斂域以及收斂區(qū)間內(nèi)的和函數(shù)3、設(shè), 將在上展為傅里葉（fourier）級數(shù)五、證明題（每小題6分，6212分）1、已知級數(shù)與都收斂，且 證明：級數(shù)也收斂2、證明： 66試題參考

3、答案與評分標(biāo)準(zhǔn)課程名稱 數(shù)學(xué)分析()適 用 時 間 試卷類別 1 適用專業(yè)、年級、班 應(yīng)用、信息專業(yè) 一、 單項選擇題（每小題3分，3618分） b b a c d d二、 填空題（每小題3分，3618分） 三、 計算題（每小題6分，6530分）1. 解 （3分） （3分）2. 解 由分部積分公式得 （3分） （3分）3. 解 令由定積分的換元積分公式，得 （3分） 67 （3分）4. 解 由洛必達(dá)(lhospital)法則得 （4分） （2分）5. 解 （2分） （2分） （2分）四、 解答題（第1小題6分，第2、3小題各8分，共22分）1. 解 （正整數(shù)） （3分）而級數(shù)收斂，故由m判別法

4、知，在區(qū)間上一致收斂 （3分） 682. 解 冪級數(shù)的收斂半徑，收斂區(qū)間為 （2分）易知在處收斂，而在發(fā)散，故的收斂域為 （2分） （2分）逐項求積分可得即 （2分）3. 解 函數(shù)及其周期延拓后的圖形如下函數(shù)顯然是按段光滑的，故由收斂性定理知它可以展開為fourier級數(shù)。 （2分）由于在為奇函數(shù)，故 而 （4分）所以在區(qū)間上， （2分） 69五、 證明題（每小題5分，5210分）1. 證明 由與都收斂知，級數(shù)也收斂。 （1分）又由 可知， 從而由正項級數(shù)的比較判別法知收斂， （2分）于是由 知級數(shù)收斂 （2分）2. 證明 令，則. （1分）由定積分的換元積分公式，得 （2分） （2分） 70

5、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 directo

6、r 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 play

7、ed 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

8、 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

9、 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, pres

10、ident 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

11、: 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,

12、 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

13、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

14、 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 expect

15、ed 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 stabi

16、lization 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 h