1、數學分析專題研究期末試題一、 填空題（每小題3分，共18分）1.若，則.2.若，則.3.設，若，有,則稱為從到上的 .4.含有 的等式叫做函數方程.5.設，則.6.設函數定義在開區間內，對于，有，則稱是內的 函數.二、 單項選擇題（每小題3分，共18分）1.設，有.a. b. c. d. 2.自然數集，是（ ）a. 有限集 b. 可列集 c. 不可列集 d. 空集3.設定義在上，是的極小值點，則（ ）a. b. 有 c. 當時，有d. 4.設是二元函數，且使得，則函數是（ ）a.有理函數 b. 無理函數 c. 代數函數 d. 超越函數5.設是內的嚴格上凸函數，則（ ）a. 在內必取到最大值 b

2、. 在內必取到最小值c. 在內有 d. 前三個結論都不對6. 在內連續可導，且，使得，則是（ ）a. 穩定點 b. 極值點 c. 拐點 d. 臨界點三、 計算題（每小題6分，共24分）1.設，求.2.已知的曲線經過點，且曲線上任意點的切線的斜率是該點橫坐標的2倍，求.3.已知，求.4.已知，求.四、 證明題（每小題8分，共32分）1.設定義在上，對于任意的，有，則是常值函數.2.證明（1） (4分)(2) （4分）3.若函數在閉區間上連續，且皆屬于，則至少存在一點，使得4.設證明答案：一、 填空題（每小題3分，共18分）1、；2、甲，乙，甲，乙；3、單射；4、未知函數；5、；6、上凸。二、 單

3、項選擇題（每小題3分，共18分）1.d;2.b;3.c;4.c;5.d;6. a.三、計算題（每小題8分，共32分）1.解 因為,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，對兩端關于求導，得 4分由 8分4、解 已知 （1）令，即，得 （2）（2）得 6分 即， 8分四、證明題（每小題8分，共32分）1、證明：對于，有 令，則得， 6分由的任意性知，。 8分2、證明：用表示的補集，則（1） = = 4分（2） = = 8分3、已知在上連續，故在有最大值與最小值，從而有 4分由介值定理，存在，使 8分4設，對于，我們有，即在內是嚴格下凸函數，故對于有 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.待添加的隱藏文字內容2cska gener

5、al director 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 ma

6、tches played 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 disc

7、rimination 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

8、 the match 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 pla

9、tini, president 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 disappoi

10、nting news: 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

11、 attached, 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

12、 into the 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 b

13、ecomes the 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

14、 is expected 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 h

15、as a stabilization 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