電大《數(shù)學(xué)分析選論》習(xí)題全解模擬試題及答案小抄參考

1、專業(yè)好文檔 數(shù)學(xué)分析續(xù)論 模擬試題及答案 一、 單項(xiàng)選擇題（） （）設(shè) 為單調(diào)數(shù)列，若存在一收斂子列，這時(shí)有 ；不一定收斂；不一定有界； 當(dāng)且僅當(dāng)預(yù)先假設(shè)了為有界數(shù)列時(shí)，才有成立 （）設(shè)在r上為一連續(xù)函數(shù)，則有 當(dāng)為開區(qū)間時(shí)必為開區(qū)間；當(dāng)為閉區(qū)間時(shí)必為閉區(qū)間；當(dāng)為開區(qū)間時(shí)必為開區(qū)間；以上、都不一定成立 （）設(shè)在某去心鄰域內(nèi)可導(dǎo)這時(shí)有 若存在，則；若在連續(xù)，則a成立；若存在，則；以上、都不一定成立 （）設(shè)在上可積，則有 . 在上必定連續(xù)；在上至多只有有限個(gè)間斷點(diǎn)；的間斷點(diǎn)不能處處稠密； 在上的連續(xù)點(diǎn)必定處處稠密 （）設(shè) 為一正項(xiàng)級(jí)數(shù)這時(shí)有 若,則 收斂；若 收斂，則；c若 收斂，則； 以上、都不

2、一定成立二、計(jì)算題（） （）試求下列極限：；（）設(shè)試求（）試求由曲線 ，直線，以及二坐標(biāo)軸所圍曲邊梯形的面積 （）用條件極值方法（lagrange乘數(shù)法）導(dǎo)出從固定點(diǎn)到直線的距離計(jì)算公式三、證明題（）（）設(shè)在上都連續(xù)試證：若，則必存在，滿足（）證明在其定義域上為一嚴(yán)格凸函數(shù)，并導(dǎo)出不等式：,其中 均為正數(shù)( 提示：利用詹森不等式)（） 證明：解 答一、答（）；（）；（）；（）；（）二、解（） ； （）1 2 （）所圍曲邊梯形如右圖所示其面積為（）由題意，所求距離的平方（）為的最小值，其中需滿足，故此為一條件極小值問題依據(jù) lagrange 乘數(shù)法，設(shè)，并令（）由方程組（）可依次解出：最后結(jié)果就

3、是所求距離的計(jì)算公式注上面的求解過程是由（）求出后直接得到，而不再去算出的值，這是一種目標(biāo)明確而又簡(jiǎn)捷的解法三、證（）只需引入輔助函數(shù)：易知在上連續(xù)，滿足，故由介值性定理（或根的存在定理），必存在，滿足，即（）的定義域?yàn)?，在其上滿足：，所以為一嚴(yán)格凸函數(shù)根據(jù)詹森不等式，對(duì)任何正數(shù)，恒有最后借助函數(shù)的嚴(yán)格遞增性，便證得不等式（）由于較難直接求出該級(jí)數(shù)的部分和，因此無(wú)法利用部分和的極限來計(jì)算級(jí)數(shù)的和此時(shí)可以考慮把該級(jí)數(shù)的和看作冪級(jí)數(shù)在處的值，于是問題轉(zhuǎn)為計(jì)算 不難知道上述冪級(jí)數(shù)的收斂域?yàn)?，?jīng)逐項(xiàng)求導(dǎo)得到；這已是一個(gè)幾何級(jí)數(shù)，其和為再通過兩邊求積分，還原得由于這里的，于是求得if we dont d

4、o 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 baba

5、ev 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 s

6、pectators 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 wash

7、ed 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 an

8、d 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 eur

9、opean 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 ab

10、orted.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 t

11、hrough 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

12、. 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 bo

13、ttom 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

14、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 par

15、achute 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 conscious