电大数学分析专题研究期末试题小抄参考

1、数学分析专题研究期末试题一、 填空题（每小题3分，共18分）1.若，则.2.若，则.3.设，若，有,则称为从到上的 .4.含有 的等式叫做函数方程.5.设，则.6.设函数定义在开区间内，对于，有，则称是内的 函数.二、 单项选择题（每小题3分，共18分）1.设，有.a. b. c. d. 2.自然数集，是（ ）a. 有限集 b. 可列集 c. 不可列集 d. 空集3.设定义在上，是的极小值点，则（ ）a. b. 有 c. 当时，有d. 4.设是二元函数，且使得，则函数是（ ）a.有理函数 b. 无理函数 c. 代数函数 d. 超越函数5.设是内的严格上凸函数，则（ ）a. 在内必取到最大值 b

2、. 在内必取到最小值c. 在内有 d. 前三个结论都不对6. 在内连续可导，且，使得，则是（ ）a. 稳定点 b. 极值点 c. 拐点 d. 临界点三、 计算题（每小题6分，共24分）1.设，求.2.已知的曲线经过点，且曲线上任意点的切线的斜率是该点横坐标的2倍，求.3.已知，求.4.已知，求.四、 证明题（每小题8分，共32分）1.设定义在上，对于任意的，有，则是常值函数.2.证明（1） (4分)(2) （4分）3.若函数在闭区间上连续，且皆属于，则至少存在一点，使得4.设证明答案：一、 填空题（每小题3分，共18分）1、；2、甲，乙，甲，乙；3、单射；4、未知函数；5、；6、上凸。二、 单

3、项选择题（每小题3分，共18分）1.d;2.b;3.c;4.c;5.d;6. a.三、计算题（每小题8分，共32分）1.解 因为,故有 5分所以有 8分2.解由方程可得，由得，即 8分3.解 已知，对两端关于求导，得 4分由 8分4、解 已知 （1）令，即，得 （2）（2）得 6分 即， 8分四、证明题（每小题8分，共32分）1、证明：对于，有 令，则得， 6分由的任意性知，。 8分2、证明：用表示的补集，则（1） = = 4分（2） = = 8分3、已知在上连续，故在有最大值与最小值，从而有 4分由介值定理，存在，使 8分4设，对于，我们有，即在内是严格下凸函数，故对于有 6分代入得 8分i

4、f 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

5、 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 playe

6、d 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

7、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

8、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, presi

9、dent 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:

10、 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,

11、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 s

12、tratosphere. 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

13、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 expecte

14、d 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 stabil

15、ization 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 conscio