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1、专业好文档数学分析-1样题(一)一. (8分)用数列极限的定义证明.二. (8分)设有复合函数, 满足:(1);(2),有(3)用定义证明, .三. (10分)证明数列:收敛.四. (12分)证明函数在一致连续,在不一致连续.五. (12分)叙述闭区间套定理并以此证明闭区间上连续函数必有界.六. (10分)证明任一齐次多项式至少存在一个实数零点.七. (12分)确定使.八. (14分)求函数在的最大值与最小值.九. (14分)设函数在二阶可导, .证明存在,使.数学分析-1样题(二)一. (10分)设数列满足: , , 其中是一给定的正常数, 证明收敛,并求其极限.二. (10分)设, 用定义
2、证明.三. (10分)设,且, 证明.四. (10分)证明函数在开区间一致连续在连续,且,存在有限.五. (12分)叙述确界定理并以此证明闭区间连续函数的零点定理.六. (12分)证明:若函数在连续,且,而函数在可导,则函数在可导.七. (12分)求函数在的最大值,其中.八. (12分)设在上是凸函数,且在可微,则对任意, ,都有.九. (12分)设 且, , 求.数学分析-2样题(一)一.(各5分,共20分)求下列不定积分与定积分:1. 2. 3. 4. 二.(10分)设是上的非负连续函数, .证明 .三. (10分)证明.四. (15分)证明函数级数在不一致收敛, 在(其中)一致收敛.五.
3、 (10分)将函数展成傅立叶级数.六. (10分)设证明: (1) , 存在;(2) ,在不连续;(3) 在可微.七. (10分)用钢板制造容积为的无盖长方形水箱,怎样选择水箱的长、宽、高才最省钢板?八. (15分)设, 证明.数学分析-2样题(二)一. (各5分,共20分)求下列不定积分与定积分:1.2. 3. 4. 二. (各5分,共10分)求下列数列与函数极限:1. 2. 三.(10分)设函数在连续,对任意上的连续函数, ,有.证明 .四. (15分)定义上的函数列证明在不一致收敛.五. (10分)求幂级数的和函数.六. (10分)用定义证明.七. (12分)求函数的极值.八. (13分
4、)设正项级数收敛,且.证明.数学分析-3样题(一)一 (10分) 证明方程所确定的隐函数满足方程二 (10分) 设个正数之和是，求函数的最大值.三 (14分) 设无穷积分收敛，函数在单调，证明 四 (10分) 求函数的导数五 (14分) 计算六 (10分) 求半径为的球面的面积.七 (10分) 求六个平面所围的平行六面体的体积，其中都是常数，且八 (12分) 求，其中是光滑的不通过原点的正向闭曲线.九 (10分) 求，其中是球面被平面所截的顶部.数学分析-3样题(二)一 (10分) 求曲面在点对应曲面上的点的切平面与法线方程. 二 (10分) 求在两个曲面与交线上到原点最近的点.三 (14分)
5、 设函数在单调减少，且，证明无穷积分与级数同时收敛或同时发散.四 (12分) 证明 五 (12分) 设函数在连续，证明，有六 (10分) 求椭圆区域的面积.七 (10分) 设，其中，是连续函数，求.八 (10分) 应用曲线积分求的原函数.九 (12分) 计算，其中是球面在部分并取球面外侧.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
6、 - 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 by the Ivorian and the British media.Blatter, 77, said: It has been decided by the Fifa congress that i
7、t 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 spirit of football and against the visiting team. It is all nonsense.We can do something better to fight ra
8、cism 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 there Watch mCayman Islands-based Webb, the head of Fifas anti-racism taskforce, is in London for the F
9、ootball 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 told BBC Sport.For me its about how he felt and I would like to speak to him first to find out what his e
10、xperience 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 ordered an immediate investigation into the referees actions.CSKA said they were surprised and disappo
11、inted 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 as early as Sunda.The weather plays an important role in this mission. Starting at the ground, condit
12、ions 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 (the troposphere) where our day-to-day weather lives. It will climb higher than the tip of Mount Evere
13、st (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 (called the tropopause),e can expect a lot of turbulence.The balloon will slowly drift to the edge of space
14、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 land on, but not too hard. Still, hell be traveling fast, so despite the distance, it will not be like
15、 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) - 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
