电大数学分析(Ⅱ)试题与参考答案小抄参考.doc

专业好文档数学分析（2）期末试题课程名称 数学分析（）适 用 时 间 试卷类别 1 适用专业、年级、班 应用、信息专业 一、单项选择题（每小题3分，3×618分）1、 下列级数中条件收敛的是（ ）A B C D 2、 若是内以为周期的按段光滑的函数, 则的傅里叶（Fourier）级数在它的间断点处 （ ）A收敛于 B收敛于 C 发散 D可能收敛也可能发散3、函数在上可积的必要条件是（ ）A有界 B连续 C单调 D存在原函数4、设的一个原函数为，则（ ）A B C D 5、已知反常积分收敛于1，则（ ）A B C D 6、收敛，则（ ）A B C 为任意实数 D 二、填空题（每小题3分，3×618分）1、已知幂级数在处条件收敛，则它的收敛半径为 2、若数项级数的第个部分和，则其通项 ，和 3、曲线与直线，及轴所围成的曲边梯形面积为 4、已知由定积分的换元积分法可得，则 ， 5、数集的聚点为 6、函数的麦克劳林（Maclaurin）展开式为 65 三、计算题（每小题6分，6×530分）1、 2、3、 4、5、四、解答题（第1小题6分，第2、3 小题各8分，共22分）1、讨论函数项级数在区间上的一致收敛性2、求幂级数的收敛域以及收敛区间内的和函数3、设, 将在上展为傅里叶（Fourier）级数五、证明题（每小题6分，6×212分）1、已知级数与都收敛，且 证明：级数也收敛2、证明： 66试题参考答案与评分标准课程名称 数学分析()适 用 时 间 试卷类别 1 适用专业、年级、班 应用、信息专业 一、 单项选择题（每小题3分，3×618分） B B A C D D二、 填空题（每小题3分，3×618分） 三、 计算题（每小题6分，6×530分）1. 解 （3分） （3分）2. 解 由分部积分公式得 （3分） （3分）3. 解 令由定积分的换元积分公式，得 （3分） 67 （3分）4. 解 由洛必达(LHospital)法则得 （4分） （2分）5. 解 （2分） （2分） （2分）四、 解答题（第1小题6分，第2、3小题各8分，共22分）1. 解 （正整数） （3分）而级数收敛，故由M判别法知，在区间上一致收敛 （3分） 682. 解 幂级数的收敛半径，收敛区间为 （2分）易知在处收敛，而在发散，故的收敛域为 （2分） （2分）逐项求积分可得即 （2分）3. 解 函数及其周期延拓后的图形如下函数显然是按段光滑的，故由收敛性定理知它可以展开为Fourier级数。 （2分）由于在为奇函数，故 而 （4分）所以在区间上， （2分） 69五、 证明题（每小题5分，5×210分）1. 证明 由与都收敛知，级数也收敛。 （1分）又由 可知， 从而由正项级数的比较判别法知收敛， （2分）于是由 知级数收敛 （2分）2. 证明 令，则. （1分）由定积分的换元积分公式，得 （2分） （2分） 70"If we don't 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 FA's 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 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 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 can be washed out of football."The (lack of) air up there Watch mCayman Islands-based Webb, the head of Fifa's anti-racism taskforce, is in London for the Football Association's 150th anniversary celebrations and will attend City's 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 it's about how he felt and I would like to speak to him first to find out what his experience was."Uefa has opened disciplinary proceedings against CSKA for the "racist behaviour of their fans" during City's 2-1 win.Michel Platini, president of European football's governing body, has also ordered an immediate investigation into the referee's actions.CSKA said they were "surprised and disappointed" by Toure's 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, 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 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 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 concrete bottom of a swimming pool that he wants to land on, but not too hard. Still, he'll 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 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 parachute that can be deployed to slow him down. His team hopes it's 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 consciousness at mach speeds.Even if everything goes as planned, it won't. Baumgartner still will free fall at a speed that would cause you and me to pass out, and no parachute is guaranteed to work higher than 25,000 feet (7,620 meters).cause there