北京理工大学2006-2007学年第一学期数学分析B期中试题

北京理工大学信息科学技术学院自动控制理论1999——2000，2002——2008自动控制理论（非控类）2004电子技术（含模拟、数字部分）1999——2000，2002——2008模拟电子技术与数字电子技术2000——2002模拟与数字电路1999——2000，2002微机控制与应用技术2002——2008控制工程基础2003——2008物理光学2003——2004，2007——2008应用光学1999——2008，2010（2010为回忆版）波动光学2002大学物理2006——2008精密机械设计2003——2008（其中2003年称“精密机械基础”）激光原理1999——2001，2005——2008电子电路2003——2005，2007——2008电路分析基础1999——2000信号处理导论2003——2008信号与系统1996——2002半导体物理学1999——2008电磁场理论1999——2000，2002——2008微机原理及应用2004——2005电动力学2003——2004理论力学1996——2008（96——98非原版）生物化学1999——2008（注：2007年试卷共11页，缺P5-6页）生物化学（A）2005——2006，2008计算机专业基础（含计算机组织与结构、数据结构）2007计算机技术基础（含计算机组成原理、操作系统和数据结构）2003——2006计算机原理（含操作系统）1999——2002程序设计1999——2000计算机系统结构基础（含计算机组成原理、计算机网络和数据结构）2004——2005 软件理论基础（含离散数学、操作系统、数据结构）1999——2005数据结构与程序设计2004——2008微波技术基础1999——2000晶体管理原理与制造1999——2000机电工程学院电子技术（含模拟、数字部分）1999——2000，2002——2008电子技术基础2007——2008自动控制理论1999——2000，2002——2008自动控制理论（非控类）2004电磁学2005——2008量子力学2005——2008运筹学2001——2008工程力学基础2007——2008流体力学基础2006工程流体力学2005数学物理方程2002——2006数学物理方法2000材料力学1997——1999，2002——2008理论力学1996——2008（96——98非原版）电动力学2003——2004微机控制与应用技术2002——2008控制工程基础2003——2008精密机械设计2003——2008（其中2003年称“精密机械基础”）应用光学1999——2008，2010（2010为回忆版）波动光学2002微机原理及应用2004——2005有机化学1997——2008无机化学（A）2003——2007无机化学（B）2003——2005，2007——2008分析化学2003——2008分析化学(A)2006物理化学2003——2008高分子物理2005——2008高分子化学及高分子物理2003——2004安全系统工程2003——2005，2008工程热力学（不含传热学）2003——2008爆炸与安全技术2005爆炸及其作用2006爆轰理论2003——2005化学2002——2005传感与测试技术2004——2005算法语言1998微波技术基础1999——2000晶体管理原理与制造1999——2000传热学2000应用电子技术2004机械与车辆工程学院电子技术（含模拟、数字部分）1999——2000，2002——2008 电子技术基础2007——2008自动控制理论1999——2000，2002——2008自动控制理论（非控类）2004机械设计2001——2008机械设计原理2001机械制造工程基础2003——2008机械制造工艺学2002理论力学1996——2008（96——98非原版）微机控制与应用技术2002——2008应用光学1999——2008，2010（2010为回忆版）电路分析基础1999——2000模拟电子技术与数字电子技术2000——2002模拟与数字电路1999——2000，2002精密机械设计2003——2008（其中2003年称“精密机械基础”）控制工程基础2003——2008微机原理及应用2004——2005工程热力学（不含传热学）2003——2008物理化学2003——2008工程力学基础2007——2008流体力学基础2006工程流体力学2005交通运输系统工程学2005，2007——2008微波技术基础1999——2000晶体管理原理与制造1999——2000数字电路与数字信号处理2008材料科学与工程学院物理化学（A）2008高分子物理2005——2008高分子化学及高分子物理2003——2004材料科学基础2003——2007材料力学1997——1999，2002——2008普通化学2008综合化学2008有机化学1997——2008无机化学（A）2003——2007无机化学（B）2003——2005，2007——2008分析化学2003——2008分析化学(A)2006理论力学1996——2008（96——98非原版）电化学原理2003——2006微波技术基础1999——2000晶体管理原理与制造1999——2000化工与环境学院自动控制理论1999——2000，2002——2008自动控制理论（非控类）2004过程控制原理2000——2005，2007——2008化工原理2002——2008有机化学1997——2008无机化学（A）2003——2007无机化学（B）2003——2005，2007——2008分析化学2003——2008分析化学(A)2006物理化学2003——2008电化学原理2003——2006环境微生物学2007——2008工程热力学（不含传热学）2003——2008微波技术基础1999——2000晶体管理原理与制造1999——2000生命科学与技术学院生物化学1999——2008（注：2007年试卷共11页，缺P5-6页）生物化学（A）2005——2006，2008分析化学2003——2008分析化学(A)2006细胞生物学2004——2006微生物学2005——2008分子生物学2007——2008有机化学1997——2008无机化学（A）2003——2007无机化学（B）2003——2005，2007——2008药理学2007信号处理导论2003——2008信号与系统1996——2002电子电路2003——2005，2007——2008物理光学2003——2004，2007——2008应用光学1999——2008，2010（2010为回忆版）波动光学2002信号理论基础2007——2008计算机专业基础（含计算机组织与结构、数据结构）2007计算机技术基础（(含计算机组成原理、操作系统和数据结构）2003——2006计算机原理（含操作系统）1999——2002程序设计1999——2000计算机系统结构基础（含计算机组成原理、计算机网络和数据结构）2004——2005 软件理论基础（含离散数学、操作系统、数据结构）1999——2005数据结构与程序设计2004——2008理学院电子技术（含模拟、数字部分）1999——2000，2002——2008大学物理2006——2008数学分析1995，1999——2000，2003——2008高等代数2003——2008电磁学2005——2008量子力学2005——2008电动力学2003——2004普通化学2008综合化学2008无机化学（A）2003——2007无机化学（B）2003——2005，2007——2008分析化学2003——2008分析化学(A)2006物理化学（A）2008物理化学2003——2008有机化学1997——2008理论力学1996——2008（96——98非原版）材料力学1997——1999，2002——2008工程热力学（不含传热学）2003——2008数学物理方程2002——2006数学物理方法2000电路分析基础1999——2000模拟电子技术与数字电子技术2000——2002模拟与数字电路1999——2000，2002激光原理1999——2001，2005——2008微机控制与应用技术2002——2008爆炸与安全技术2005爆炸及其作用2006电化学原理2003——2006工程力学基础2007——2008流体力学基础2006工程流体力学2005微波技术基础1999——2000晶体管理原理与制造1999——2000管理与经济学院宏微观经济学2008管理学2003——2008（2003，2004名称叫做“管理学基础”。

2008级《概率论》期末试题A 卷一、从1到30的整数中，不放回地任取3个数，求所取的3个数之和能被3整除的概率。

二、设袋中有9个红球和6个白球，不放回地任取两次，每次取两个球。

（1）求第二次取出的两个球都是白球的概率；（2）已知第二次取出的两个球都是白球，求第一次恰好取出一个红球和一个白球的概率。

三、设随机变量X 的密度函数为()2,1Af x x R x =∈+。

（1）求A 的值；（2）求21Y X =+的密度函数；（3）求概率()2P X X >。

四、设二维随机变量（X,Y ）在区域(){},|02G x y x y =<<<上服从均匀分布。

（1）写出X ，Y 的联合密度函数(),f x y ；（2）求X,Y 的边际密度函数()(),X Y f x f y ，并判断X,Y 是否独立； （3）求概率()1P X Y +<。

五、设随机变量X 的密度函数为(),00,0x e x f x x λλ-⎧>=⎨≤⎩，求,ED 。

六、设随机变量X 服从参数为1的指数分布，Y 服从正态分布()22,3N ，且X,Y 相互独立。

（1）求()2E X Y -；（2）设,3U XY V X ==，求()cov ,U V 。

七、设随机变量X 的分布律为()1,0,1,,1P X k k n n===⋅⋅⋅-，Y 服从[]0,1上的均匀分布，且X,Y 相互独立。

令Z=X+Y ，利用特征函数法证明Z 服从[]0,n 上的均匀分布。

八、设某种电子元件的寿命服从指数分布，其平均寿命为400小时。

现购买100只这种电子元件，假设它们的寿命相互独立，求这些电子元件的寿命总和在32000小时至48000小时之间的概率。

（1）用切比雪夫不等式计算；（2）用中心极限定理计算。

2010级《概率论》期末试题A 卷一、（10分）从1到9这9个数中，有放回地取3次，每次取一个，求所取的3个数之积能被10整除的概率。

北京理工大学2006年Part ⅠReading Comprehension (40 points)Directions: In this part there are four passages for you to read. After each passage there are five questions, below each of whom there are four answers marked A, B, C and D. Chouse the best answer and mark the corresponding letter with a pencil on the Machine-Scoring Answer Sheet with a single line through the center.Passage OneI was introduced to the concept of literacy animator in Oladumi Arigbede's (1994) article on high illiteracy rates among women and school dropout rates among girls. According to Arigbede, literacy animators view their role as assisting in the self-liberating development of people in the world who are struggling for a more meaningful life. Animators are a family of deeply concerned and committed people whose gut-level rejection of mass human pauperization compels them to intervene on the side of the marginalized. Their motivation is not derived from a love of literacy as merely another technical life skill, and they accept that literacy is never culturally or ideologically neutral.Arigbede writes from her experiences as an animator working with women and men in Nigeria. She believes that literacy animators have to make a clear choice about whose culture and whose ideology will be fostered among those with whom they work. Do literacy educators in the United States consider whether the instruction they pursue conflicts with their students' traditional cultures or community, or fosters illiteracies in learners' first or home languages or dialects and. in their orality?Some approaches to literacy instruction represent an ideology of individualism, control, and competition. Consider, for example, the difference in values conveyed and represented when students engage in choral reading versus the practice of having one student read out loud to the group. To identify as a literacy animator is to choose the ideology of "sharing, solidarity, love, equity, co-operation with and respect of both nature and other human beings". Literacy pedagogy that matches the animator ideology works on maintaining the languages and cultures of millions of minority children who at present are being forced to accept the language and culture of the dominant group. It might lead to assessment that examines the performance outcomes of a community of literacy learners and the social significance of their uses of literacy, as opposed to measuring what an individual can do as a reader and writer on a standardized test. Shor (1993) describes literacy animators as problerm-posing, community-based, dialogic educators. Do our teacher-education textbooks on reading and language arts promote the idea that teachers should explore problems from a community-based dialogic perspective?1. A literacy animator is one who ______.A. struggles for a more meaningful lifeB. frees people from poverty and illiteracyC. is committed to marginalize the illiterateD. is concerned with what is behind illiteracy2. The author suggests that literacy educators in the US in a way ______.A. promote students' home languagesB. force students to accept their cultureC. teach nothing but reading and writingD. consider literacy as of non-neutral nature3. Arigbede worked with Nigerians probably to ______.A. teach American customs and ideologyB. make a choice of culture to be fosteredC. reject the values of the dominant classD. help maintain Nigerian language and culture4. According to the author, "choral reading" may represent ______.A. individualismB. collectivismC. competitionD. immersion5. Animator ideology emphasizes more on ______.A. the social function of literacyB. students' performance in testsC. the dominant group's languageD. the attainment of life skillsPassage TwoAccording to one survey of 12, 000 people, about 30 percent of those making New Year's resolutions say they don't even keep them into February. And only about 1 in 5 actually stays on track for six months or more, reports eDiets, com, a consumer diet and fitness Web site.But don't let those odds make you reach for the nearest bag of potato chips. Experts say you can keep those resolutions long term, even if you're struggling now."The motivation comes from within, and so when you find that you're declining in your healthy eating program, and then just ask yourself, 'Is this going to get me the results that I want?'" says Leslie Stewart, a registered dietitian and licensed nutritionist."And if you're doing something every day to eat healthy, then that's going to pay off in the long run."Stewart advises to use what she calls the 90 -10 eating rule."If you're eating healthy 90 percent of the time, then 10 percent of the time, you can cut yourself some slack and eat pleasurably."She says she believes that "healthy eating is evolution instead of resolution."The same principle can be applied to a lagging exercise resolution, too.Staying motivated is key to long-term success, and reviewing original goals can help strengthen a weakening workout program.Adding variety to a fitness regime also can prevent you from hanging up those exercise shoes. After a few weeks of well-intentioned workouts, boredom may be creeping into your routine.Setting goals too high is another common mistake, "If you're not running a marathon at the end of the month, don't worry," said Mayo Clinic experts. A too intense workout—and the resulting pain and stiffness—is discouraging and may force most to abandon a program. Starting slowly is key.But if your goals already have fallen by the wayside, Uria says to start up again immediately."A little setback is OK; get back on the horse and ride... drive toward that goal," he says.6. According to the author, only about 20% people keeping their resolutions does not necessarily mean that ______.A. the figure is rather depressing and unexpected as wellB. those who have made their resolution should give up their effortC. whoever keep their resolutions should start eating potato chipsD. long-term resolutions are not important for those facing troubles7. What is the idea behind the 90-10 eating rule acording to the passage?A. You should keep eating healthy 90% of the time.B. You should feel to eat 10% of the time.C. You should learn to eat healthy gradually.D. Sudden change will be more efficient and effective.8. Which of the following you should avoid to keep yourself interested in exercise?A. Hanging up your exercise shoes if you feel tired.B. Keeping boredom away from your daily activity.C. Making a schedule with too high goals in it.D. Running a marathon at the beginning of the month.9. How many suggestions at least have been introduced concerning the exercise resolution?A. FourB. FiveC. SixD. Seven10. What is critically important in making long-lerm resolutions successful?A. You should be struggling with yourself all the time.B. You should constantly evaluate the results you want.C. You should try to keep yourself motivated.D. You should try your best to diversify your fitness practice.Passage ThreeOur present generation of cultural critics, arriving after the assault of postmodernism and the increasingly widespread commercialization of culture, has been cast adrift, without any firm basis for judgments. Publications and institutions to support serious criticism, in this view, either no longer exist or are few in number.Critics today, it is also claimed, are too cozy behind the ivied walls of academe, content to employ a prose style that is decipherable only to a handful of the cognoscenti. The deadly dive of Uniersity critics into the shallow depths of popular culture, moreover, reveals the unwillingness of these critics to uphold standards. Even if the reasons offered are contradictory, these Jeremiahs huddle around their sad conclusion that serious cultural criticism has fallen into a morass of petty bickering and bloated reputations.Such narratives of declension, a staple of American intellectual life since the time of the Puritans, are misplaced, self-serving, and historically inaccurate, so difficult to prove. Has the level of criticism declined in the last 50 years? Of coarse the logic of such an opinion depends on the figures that are being contrasted with one another. Any number of cultural critics thriving today could be invoked to demonstrate that cultural criticism is alive and well.But many new and thriving venues for criticism and debate exist today, and they are not limited solely t6 the discussion of literary works. Actually, they became so entrusted with their own certitude and political judgments that they beacme largely irrelevant. Today the complaint is that literary culture lacks civility. We live in an age of commercialism and spectacle. Writers seek the limelight, and one way to bask in it is to publish reviews that scorch the landscape, with Dale Peck as the famous, but not a typical case in point. Heidi Julavits, in an essay in The Believer, lamented the downfall of serious fiction and reviewing. She surveyed a literary culture that had embraced "snark", her term for hostile, self-serving reviews.The snark review, according to Julavits, eschews a serious engagement with literature in favor of a sound-bite approach, an attempt to turn the review into a form of entertainment akin to film reviews or restaurant critiques. A critic found cultural criticism to be in "critical condition". For him, the postmodern turn to theory, in its questioning of objectivity, cut the critical, independent ground out from under reviewers. The rise of chain bookstores and blockbuster best sellers demeaned literary culture, making it prey to the commercial values of the market and entertainment.The criticism does not seem discontinuous. Nor should we forget that civility rarely reigned in the circles of New York intellectuals. The art critic Clement Greenberg physically pummeled the theatre critic Lionel Abel after Abel rejected the view that Jean Wahl, the French philosopher, was anti-Semitic. Though Robert Peck has the reputation of a literary hatchet man, so far as I know his blows thus far have all been confined to the printed page.Cultural criticism has certainly changed over the years. The old day's of the critic who wielded unchallenged authority have happily passed. Ours is a more pluralistic age, one not beholden to a narrow literary culture. The democratization of criticism—as in the Amazon system of readers' evaluating books—is a messy affair, as democracy must be. But the solution to the problems of criticism in the present is best not discovered in the musty basements of nostalgia and sentiment for the cultual criticism of a half-century gone. Rather the solution is to recognize, as John Dewey did almost a century ago, that the problems of democracy demand more democracy, less nostalgia for a golden age that never was, and a spirit of openness to what is new and invigorating in our culture.11. What is the possible connection between cultural critics and publications and institutions?A. Cultural critics attack postmodernism and commercialization cherished by publications and institutions.B. Postmodernism and commercialization are attacked by the serious publications and institutions.C. Cultural criticism is short of judgments and will not exist without the support of publications and institutions.D. Publications and institutions show almost no interest in serious cultural criticism.12. How do the university critics like the serious cultural criticism?A. Cultural criticism is not serious enough when the articles are written in the cozy prose style.B. Popular culture is so prevailing that serious critics are not willing to keep to the shallow standards.C. Serious cultural criticism is full of insignificant quarrels and the public do not really trust it.D. Cultural critics have become so serious as to tell the stories imbued with American intellectual Puritanism.13. What is the author's opinion of the current complaint about the literary expansion into the other fields?A. When literary critics discuss issues with political judgments, their views are likely to be meaningless.B. It is reasonable for writers to seek limelight since we are living in the age of commercialism.C. Critics should be encouraged to write and publish poignant articles which would scorch the landscape.D. It is the critics' responsibility to lament the downfall of serious fiction and reviewing.14. What does "the snark review" refer to according to Heidi Julavits?A. Cultural reviews which are unfriendly and selfless.B. Literary reviews avoiding serious criticism.C. Entertainment reviews in the film industry.D. Postmodern reviews independent of objectivity.15. In order to find a way out the current dilemma for the cultunal criticism, the author suggests that ______.A. we should return to the old days when the critics passed their judgments without challengesB. pluralism should be held back, reinforcing the unchallenged authority in the literary criticismC. democriatic criticism should not be adopted because it is rather messy as proved in the Amazon systemD. we should encourage more democracy, dismiss nostalgia and cultivate an open attitudePassage FourIn July, almost unnoticed by the national press, a deadly bird virus arrived on a pheasant farm in Surrey. Experts from the Department for the Environment, Food and Rural Affairs (Defra) identified Newcastle disease, a virus usually mortal to turkeys and geese but not humans, in a flock of 9,000 pheasant chicks imported from France ahead of the shooting season.Within hours of the diagnosis, veterinary experts had swung into action, throwing up a 3km exclusion zone around the farm near Cobham and culling 10,000 birds. The carcasses were burned and premises cleaned to stop the virus escaping. It was four weeks before Defra's Veterinary Exotic Diseases Division felt it was safe for poultry move virus has reached Turkey, similar emergency plans are being readied by officials from Defra and other agencies. The scenario they are preparing for is that the H5Nlvirns, which so far has led to the culling of billions of chickens in south-east Asia and 60 human deaths, will soon arrive on these shores.What happens next depends on where the outbreak occurs, whether it can be contained, and most important of all—whether it mutates to become infectious between people. So far, only poultry workers or those directly exposed to chicken faeces or blood are thought to be at risk, though direct human-to-human transmission cannot be ruled out."Every time a new person gets infected with the virus there is a small chance that person will trigger a pandemic," said Neil Ferguson, a scientist at Imperial College, who has been running simulations on what might happen were H5N1 to reach Britain. "It's a very small chance, probably 1 in a 1,000, 1 in 10,00O or less."Should diseased birds reach Britain, the first step for veterinary officials would be to contain the outbreak as they did with Newcastle disease. An amber alert would be sounded and samples sent to the Veterinary Laboratory Agency (VLA) in Weybridge, Surrey. If lan Brown, the head of avian virology, there, confirms the cause of death as HSN1, the alert level will be raised to red and a whole series of emergency procedures, from quarantine,restriction of poultry movements to culling, will swing into action. Other agencies, such as the Department of Health—the Health Protection Agency and the Ministry of Defence, would be brought into the loop. In the event that the outbreak cannot be contained, Defra may have to consider mass culling programmes and the possibility of vaccination.At this point, with the risk of the virus spreading to human populations, the Department of Health would appoint a UK national influenza pandemic committee to coordinate the response of hospital trusts and local authorities. The Civil Contingency Secretariat (CCS) of the Cabinet will also be alerted and Cobra, the emergency committee which coordinates Whitehall's response to terrorism, readied for a possible breakdown in civil order.The Department of Health's pandemic preparedness plan published in March envisages as many as 54,000 Britons dying in the first few months of a flu pandemic. But in June, CCS officials warned that that could be an underestimate. The more likely figure, they said, was 700,000—a projection the Department of Health is expected to take on board when it updates its pandemic plan later this month.In the most serious case, officials estimate there would be as many death sin the 12 weeks of an epidemic as there usually are in a year. At the peak of the pandemic, 19,000 people would require hospital beds, prompting councils to requisition schools to accommodate the sick.To treat the dying, the government would begin drawing down its stockpiles of Tamiflu (药名), an anti-viral drug that treats flu. But with only 14m courses, enough for a quarter of the population, likely to be available, sooner or later rationing would have to be imposed, with health professionals and essential civil servants the first in line. The govenment would also come under pressure to release stores of its precious flu vaccine. At present there are contingency plans for just two to three million doses. But there is no guarantee that vaccines which protect against annual human flu strains will also work against H5N1.The consequences hardly bear thinking about. Earlier this year, in a dress rehearsal in the East Midlands codenames Operation Arctic Circle, officials quickly concluded that mass mortuaries would be needed to bury the dead. But no one knows whether, in the event of a pandemic, any of these measures will prove effective. John Avizienius, senior scientific officer at the RSPCA and a member of Defra's avian influenza stakeholder group, said: "All you can do is plan for the worst case scenario."The fear is that wild geese moving from western China to Siberia may have spread the virus to several species of ducks and gulls that briefly visit British shores on their annual migration north. These ducks, many of which may not show signs of illness, may be passing on the virus to poultry on British farms.In the hope that they are not, Defra and the Wildfowl and Wetland announced last week that they would be conducting tests on 11,000 wild birds—three times the normal level. "The risk of avian influenza spreading from eastern Russia to the UK via migrating birds is still low," said Defra's chief vet, Debby Reynolds. "However, we have said all along that we must remain on the look out."16. What does the "scenario" in Para. 2 mean to Turkey?A. Turkey will be exposed to the nationwide aggression of the deadly virus as the most severely attacked country on these shores.B. Turkey must kill billions of chicken and other kinds of poultry.C. Turkey has to be responsible for the arrival of HSN1 on these shores.D. All the veterinary experts in Turkey will soon swing into action.17. What is, according to Nell Ferguson, the possible risk of bird flu if one gets infected?A. Anyone's infection will trigger pandemic though it is probably one in ten thousand.B. That each time a person gets infected with the virus will cause an enormous pandemic bird-flu.C. The person infected with the virus will do great harm to people around him.D. It is impossible that the virus infection of a certain person will cause a national bird virus spreading.18. The change of alert colors from amber to red implies that ______.A. all poultry workers must leave their working places as soon as possible.B. the officials in the Department of Health must call for much more of international assistance.C. the most serious situation of bird-flu has appeared.D. the change of the color functions greatly as the weather reports do.19. What are the steps taken by the Department of Health of UK with the risk of the virus spreading to human population?A. The Department of Health required Civil Contingency Secretariat to publish documents for the pandemic preparedness.B. The Department of Health required the UK national committee to co-work with hospital trusts and local authorities.C. The Department of Health required Civil Contingency Secretariat to make a pandemic plan as soon as possible.D. The Department of Health requires every hospital to store Tamiflu, the precious flu vaccine.20. British government's fear of the wild geese from western China to Siberia is due to ______.A. the domestic ducks and gulls infected by the imported geese to Britain.B. the poultry on British farms has been infected by the immigrated wide geese.C. the migration of the wild geese every winter.D. British shores infected by the geese virus.Part ⅡTranslation (40 points)Part A Translate the following short paragraphs into Chinese. (20 points)21. Everyone has something they are ashamed of, afraid of or that they feel guilty about. Each of us, in our own way, has devised a neat little method of handling our dark side. We may know how to hide it. Few of us know how to heal it. When we refuse to admit what we have done in the past, we block out path to the future. No matter how terrible we think we are, how bad we belive we have been, how law we think we have fallen, we can clean our minds and begin again.22. We expend so much energy trying to fix who we are, we rarely get to know ourselves. If we realized how precious the gist of life is, we would not waste a moment trying to improve it. If we really understood how precious we are to the gift of life, we would not waste time trying to fix ourselves.23. We cannot draw to us more than we believe we are worth. Everything that happens to us and every choice we make is a reflection of what we believe about who we are. Our inspiration comes from our self-acceptance. Our motivation comes from our self-reliance. When we accept ourselves and rely on ourselves, we feel good about ourselves. When you feel good about something, you believe in it. When you believe in it, it will work for you!24. It is of little consequence what your past has been. What matters to you and for you is right now. It is not your concern what others may be saying or doing. When you are taking care of yourself, you have very little time to pay attention to others. People can love you or hate you, ignore you or dote on your every word. No matter what anyone else may think or do or say, it has very little impact on who you really are. It is only in your mind that you build or destroy the esteem for your "self". Selfesteem begins and ends with you. When you have it, you have it and no one can take it away from you.Part B Translate the following paragraph into English.现在，成千上万的美国人沉湎于对身材苗条的追求之中。

北京化工大学20062006——————20072007学年第一学期《高等数学》（上）期中考试试卷一、填空（每空3分，分，33分×分×27=8127=81分）1．设xx f e )(=，x x x g ln )(=，其中0>x ，1¹x ，则())(x g f = 。

2．设x x x x f e 1)e 1()(+-=，判断)(xf 的奇偶性，则)(x f 是 函数。

函数。

3．曲线x y sin =在p =x 处的切线方程是处的切线方程是 。

4．已知)(x y y =是由方程yx y e 1+=所确定的隐函数，则=)0('y 。

5．设x x x f sin )(=，2x u =，则u f d d = 。

6．设xx x f ÷øöçèæ+=11)(，其中0>x ，则)('x f = 。

7．设ïîïíì-=-=321tt y t x ，则22d d x y = 。

8．设21arcsin x y -=，其中0>x ，=y d 。

9．在括号中填入适当的函数d ( )=x x d 3sec 21010．．()x x x x x --++¥®l imlim = 。

11．x x x x x 20sin cos 1)1(ln )1(ln lim +--++®= 。

12．x x x tan 2)(sin lim p®= 。

13．已知当0®x 时，2~1ln kx x x +，则k = 。

14．1ln 2)(--=x x x f 的一个无穷间断点为x = 。

15．设)1(e )(--=x x a x f x ，已知1=x 为可去间断点，则0=x 是第是第 类间断点。

类间断点。

16．函数xx f 2)(=的n 阶麦克劳林公式的拉格朗日型余项是阶麦克劳林公式的拉格朗日型余项是 。

北京交通大学2006----2007学年第一学期《随机数学》期中考试试卷一、本题满分30分，每小题5分1.设事件A，B，C两两独立，且解：2. 从混有5张假钞地20张百元钞票中任意抽出2张，并将其中1张拿到验钞机上检验，结果发现是假钞，求抽出地2张都是假钞地概率.解：A=“抽出地2张中至少有一张是假钞”， B=“抽出地2张全是假钞”，3.设随机变量X地概率密度函数，若数a使，求a.解：显然，且4．已知随机变量X地可能取值为-1，0，1，2，其相应地概率依次为<1）求c地值；<2）求X地分布函数解：<1）由分布律地性质，知<2）5．某种布每平方M地疵点数X服从地泊松分布，求每平方M这种布地疵点数多于1不超过4地概率.解：X地分布律：，P{每平方M这种布地疵点数多于1不超过4}=6．设随机变量相互独立，且都服从参数为5地指数分布，求；解： ,二．本题满分40分，共有5道小题，每道小题8分．7. 设某城市男子身高<单位cm），若公共汽车车门地高度为176cm, 求3个男子同时乘车至少有1人与车门碰头地概率.解：任一男子身高超过176地概率为：Y=“3个男子同时乘车与车门碰头地人数”，则B=“3个男子同时乘车至少有1人与车门碰头”8．对圆片直径进行测量，测量值，求圆片面积Y地概率密度.解：X地概率密度，时，严格单增处处可导，其反函数为，时，，圆片面积Y地概率密度9．甲、乙两人约定在某地相会，假定每人地到达时间是相互独立地，且均服从中午12时到下午1时地均匀分布.试求先到者需等待20分钟以内地概率.解；设甲于12时X分到达，乙于12时分到达，则X，Y相互独立，且都服从[0，60]上地均匀分布.，A=“先到者等待20分钟” =10．设二维随机变量<X，Y）地概率密度函数为求随机变量地概率密度函数.解：，11．设随机变量X和Y相互独立，且，，<1）求p地值； <2）求X和Y地联合分布律；<3）求Z=max(X,Y> 地分布律.解：<1），，， .<2），，<3），，三．本题满分30分，共有3道小题，每道小题10分）．12．设有来自三个地区地各10名、15名和25名考生地报名表，其中女生地报名表分别为3份、7份和5份.随机地取一个地区地报名表，从中先后抽出两份.（1）求先抽到地一份是女生表地概率；（2）已知先抽到地一份是女生表，求后抽到地一份是男生表地概率.解：{第次抽到地一份是女生表}{报名表是来第自地区地}，，，<1）由全概率公式<2），13．设二维随机变量<X，Y）地概率密度函数为<1）. 求边缘概率密度函数.； <2）判断X和Y是否相互独立；<3）求； <4）求.解：<1），，，<2）故X和Y相互独立.<3），<4）14．设随机变量X地概率密度函数定义随机变量为：，<1）求二维随机变量地联合分布律，以及各自地边缘分布律；<2）求W=UV地分布律.解：<1），<2）地可能取值 -1，1申明：所有资料为本人收集整理，仅限个人学习使用，勿做商业用途.。

2006——2007学年第二学期数学分析试题Ｂ答案（0601，0602，0603）一：填空（20分）1. 12. ≤3. 1、04. 05. ''()()x t y t 与不同时为06. ()x e C ϕ+7. 绝对收敛8. 1p >9. 充要条件 10.[,]a b 二：判断（16分）⨯∨⨯∨∨⨯⨯⨯三：计算下列各题（15分）2222212221()(3)21241)241(1) (5)22x x x x x x C ====-+⎰⎰分分分2令6x u =则原式变为523216(1)(3)16(ln |1|)326ln |1| 5u u du u u u u u C C ==-+-+=-+-++=+⎰⎰分（分）2020220020cos 3sin cos 1cos sin sin cos (3)2sin cos 11(sin cos )22sin cos (ln |sin cos |)| (4)44d d d d πππππθθθθθθθθθθθθθθθθπθθπ++-+=++=++=+=⎰⎰⎰⎰分分 (5)分四：解下列各题（28分）1、求幂级数 +++++++12531253n x x x x n )1,1(-∈x 的和函数0011,12121n n n x n n ∞∞====±++∑∑2n+1(-1)解：因且，与都是发散级数该幂级数的收敛区域为(1,1)- （4分）设3521()3521n x x x F x x n +=++++++在收敛区域||1x <内逐项微分之，得'2321()11F x x x x =+++=- （5分） 注意(0)0F =，即得2011()ln (||1)121xdt xF x x t x+==<--⎰于是当||1x <时，有352111ln (||1)352121n x x x x x x n x+++++++=<+- （7分）2、计算⎰⎰⎪⎭⎫ ⎝⎛∞→x t x t x dte dt e 022022lim 解：该极限是∞∞型的不定式极限，利用洛必塔法则有 ()22222222222020lim2lim(3)2lim (5)2lim20 (7)x t xx t x xt x x xt x x xxx e dt e dte e dtee dte e xe →∞→∞→∞→∞====⎰⎰⎰⎰分分分112(1)3lim sin sin sin1(1)lim sin (3)n n n i n n n n n i n n ππππππ→∞→∞=-⎛⎫+++ ⎪⎝⎭-=⋅∑分其中的和式是()sin f x x =在区间[0,]π上的一个积分和，这里所取的是等分分割，(1),i i i x nn ππξ-∆==为小区间1,(1)[][,]i i i i x x n nππ--=的左端点，1,2,,i n =故有12(1)lim sin sin sin1sin (6)n n n n n n xdxπππππ→∞-⎛⎫+++ ⎪⎝⎭=⎰分1(cos )|2(7)x πππ=-=分4 解：为方便起见。