2016年電大《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、PAGE 數(shù)學(xué)分析續(xù)論 模擬試題及答案 單項選擇題（） （）設(shè) 為單調(diào)數(shù)列，若存在一收斂子列，這時有 ；不一定收斂；不一定有界； 當且僅當預(yù)先假設(shè)了為有界數(shù)列時，才有成立 （）設(shè)在R上為一連續(xù)函數(shù)，則有 當為開區(qū)間時必為開區(qū)間；當為閉區(qū)間時必為閉區(qū)間；當為開區(qū)間時必為開區(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間斷點；的間斷點不能處處稠密； 在上的連續(xù)點必定處處稠密 （）設(shè) 為一正項級數(shù)這時有 若,則 收斂；若 收斂，則；C若 收斂，則； 以上、都不一定成立

2、二、計算題（） （）試求下列極限：；（）設(shè)試求（）試求由曲線 ，直線，以及二坐標軸所圍曲邊梯形的面積 （）用條件極值方法（Lagrange乘數(shù)法）導(dǎo)出從固定點到直線的距離計算公式三、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)果就是所求距離的計算公

3、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，這是一種目標明確而又簡捷的解法三、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（）的定義域為，在其上滿足：，所以為一嚴格凸函數(shù)根據(jù)詹森不等式，對任何正數(shù)，恒有最后借助函數(shù)的嚴格遞增性，便證得不等式（）由于較難直接求出該級數(shù)的部分和，因此無法利用部分和的極限來計算級數(shù)的和此時可以考慮把該級數(shù)的和看作冪級數(shù)在處的值，于是問題轉(zhuǎn)為計算 不難知道上述冪級數(shù)的收斂域為，經(jīng)逐項求導(dǎo)得到；這已是一個幾何級數(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 do that it

4、 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 Babaev says t

5、he 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

6、 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

7、 football.The (lack of) air up there HYPERLINK /2012/10/13/opinion/jones-baumgartner-skydive/index.html?hpt=hp_c1Watch 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 m

8、atch 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 experience was.Uefa has HYPERLINK http:/www.bbc.co.uk/sport/0/football/24654499opened disci

9、plinary proceedings against CSKAfor the racist behaviour of their fans during HYPERLINK http:/www.bbc.co.uk/sport/0/football/24615218Citys 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

10、 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 aborted.The supersonic descent could happen as early as Sunda.The weather plays an important role in this mission. Starting

11、 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

12、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

13、 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, hell be traveling fast, so despite the distanc

14、e, it will not be like diving into the deep end of a pool. It will be like he is diving into the shallow end. HYPERLINK /2010/US/05/21/supersonic.skydive/index.htmlSkydiver 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

15、. 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 its n

16、ot 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

17、consciousness at mach speeds.Even if everything goes as planned, it wont. 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 表4 電子商務(wù)網(wǎng)站的維護表項目說明網(wǎng)站基本內(nèi)容的維護工作及有關(guān)數(shù)據(jù)的備份工作公司新聞的管理及維護向網(wǎng)站

18、上傳公司最新的新聞、公告等產(chǎn)品資料的管理及維護向網(wǎng)站上傳宣傳彩頁等資料，圖片處理等 網(wǎng)站域名、主機維護、企業(yè)郵局的管理與維護包括國際域名續(xù)費、轉(zhuǎn)移注冊商，國內(nèi)域名續(xù)費；網(wǎng)站資料備份服務(wù)定期對資料進行整理備份；及時查看回復(fù)留言反饋定期查看網(wǎng)站留言，并對有關(guān)問題進行回復(fù)網(wǎng)站流量統(tǒng)計報告服務(wù)進行網(wǎng)站流量統(tǒng)計 每月提供工作報告詳細介紹每月工作進展情況 在售商業(yè)地理位置建筑面積（）業(yè)態(tài)價格營銷模式開發(fā)商奧特萊斯購物廣場城西區(qū)濠西路299號一期70000名牌折扣、工廠直銷的主力業(yè)態(tài)，兼具購物、休閑、餐飲、娛樂功能總體均價1、5萬/ 1層2.2萬/左右；2層1.5萬/左右；三層整層出售開發(fā)商統(tǒng)一運作；7%租金返租3年，房款總價中扣除江蘇新海