2016年山东科技大学考研真题708数学分析硕士研究生专业课考试试题
山东科技大学考研真题
Part I Reading Comprehension (2*25=50 points)Directions: There are five passages in this section. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Decide on the best choice.Passage 1Children learn almost nothing from television, and the more they watch the less they remember. They regard television purely as entertainment, resent programs that demand on them and are surprised that anybody should take the medium seriously. Far from being over-excited by programs, they are mildly bored with the whole thing. These are the main conclusions from a new study of children and television. The author——Cardiac Cullingford confirms that the modern child is a dedicated viewer. The study suggests that there is little point in the later hours. More than a third of the children regularly watch their favorite programs after 9 p.m. All 11-year-olds have watched programs after midnight.Apart from the obvious waste of time involved, it seems that all this viewing has little effect. Children don’t pay close attention, says Cullingford, and they can recall few details. They can remember exactly which programs they have seen but they can rarely explain the elements of a particular plot. “Reca ll was in reverse proportion to the amount they had watched”. It is precisely because television, unlike a teacher, demands so little attention and response that children like it, argues Cullingford. Programs seeking to put over serious messages are strongly disliked. So are people who frequently talk on screen. What children like most, and remember best, are the advertisements. They see them as short programs in their own right and particularly enjoy humorous presentation. But again, they react strongly against high-pressure advertisements that attempt openly to influence them.On the other hand, they are not emotionally involved in the programs. If they admire the stars, it is because the actors lead glamorous lives and earn a lot of money, not because of their fictional skills with fast cars and shooting villains. They are perfectly clear about the functions of advertisements; by the age of 12, only one in 10 children believes what even favorite ads say about the product. And says Cullingford, educational television is probably least successful of all in imparting attitudes or information.1. The study of children and television shows that_______.A. it is useless for television companies to delay adult viewing to the later hours.B. It is a waste of time for children to watch adult programs on TV.C. Children should not watch television programs late into the night.D. Children are supposed to learn a lot from television programs.2. “Recall was in reverse proportion to the amount they had watched” (in Para.2) has almost the same meaning as________.A. “the more they watch the less they remember”. (in Para. 1)B. “Programs seeking to put over serious messages are strongly disliked”. (in Para. 2)C.“They see them as short programs in their own right”. (in Para. 2)D. “educational television is probably least successful of all in imparting attitudes or information”. (in Para. 3)3. Which of the following is NOT true according to the new study of children and television?A. Some children stay up late to watch the programs they likeB. Children enjoy watching challenging programs.C. Children don’t like serious messages and high-pressured ads.D. Though children like watching ads, most of them don't believe what ads say about the product.4. Cullingford concludes that_______.A. children are excited when they watch TV.B. Watching TV has little real effect on children.C. Parents should spend less time watching TV.D. Parents should be worried about the effect of TV on children.5. Whom would the result of the new study upset?A. The advertisers.B. The children viewers.C. The movie stars.D. The educators.Passage 2Mrs. Lester kept on asking her husband to take her to the ballet. Mr. Lester hates the ballet, but when his employers invited him and his wife, he could not get out of it. As they drove to the theatre that evening, the fog got worse and worse. The traffic slowed down to a walking pace and almost stopped. When they eventually got to the theatre, the ballet was over. Mrs. Lester could not work out how it had taken them so long to get there, even taking the fog into account. The theatre was within walking distance of their house. It took her a long time to get over the disappointment.A month later, Mrs. Lester found out what had happened. Mr. Lester told a friend of his that he had taken wrong turning on purpose. This friend told his wife, and the wife immediately went around to tell Mrs. Lester. The two women began to plan revenge. One day, when Mr. Lester was not in, they broke into his study, which he always locked. His hobby was collecting old coins. Mrs. Lester had already worked out how much his collection was worth: $850! They were taking some coins out of the case when they heard a car pull upoutside the house. Mrs. Lester quickly switched the light off, and they waited, holding their breath. The front door opened and Mr. Lester came in. They heard him take his coat off. He walked towards the study door and opened it. There was no chance for the women to get away without being seen. Mr. Lester switched the light on and was astounded to see his wife standing there with a handful of valuable coins. It took both husband and wife a long time to get over this.6. Which of the following is correct?A. Mr. Lester likes to watch ballet.B. Mrs. Lester likes to watch ballet.C. Both of them like to watch balletD. Neither of them likes to watch ballet.7. It was quite ____when they drove to the theatre.A. rainyB. stormyC. cloudyD. foggy8. The theater is _____from Mr. and Mrs. L ester’s.A. an hour-drivingB. in the other side of the cityC. very nearD. half an hour of bicycle riding9. The wife of Mr. Lester’s friend is a_____.A. social workerB. house cleanerC. baby sitterD. gossip10. How many persons are mentioned in this story?A. ThreeB. FourC. FiveD. Six.Passage 3Educating girls quite possibly yields a higher rate of return than any other investment available in the developing world. Women’s education may be unusual terri tory for economists, but enhancing women’s contribution to development is actually as much an economic as a social issue. And economics, with its emphasis on incentives, provides guideposts that point to an explanation for why so many girls are deprived of an education.Parents in low-income countries fail to invest in their daughters because they do not expect them to make an economic contribution to the family: girls grow up only to marry into somebody else’s family and bear children. Girls are thus se en as less valuable than boys and are kept at home to do housework while their brothers are sent to school-the prophecy becomes self-fulfilling, trapping women in a vicious circle of neglect.An educated mother, on the other hand, has greater earning abilities outside the home and faces an entirely different set of choices. She is likely to have fewer but healthier children and can insist on the development of all her children, ensuring that her daughters are given a fair chance. The education of her daughters then makes it much more likely that the next generation of girls, as well as of boys, will be educated and healthy. The vicious circle is thus transformed into a virtuous circle.Few will dispute that educating women has great social benefits. But it has enormous economic advantages as well. Most obviously, there is the direct effect of education on the wages of female workers. Wages rise by 10 to 20 per cent for each additional year of schooling. Such big returns are impressive by the standard of other available investments, but they are just the beginning. Educating women also has a significant impact on health practices, including family planning.11. The author argues that educating girls in developing countries is _______.A. rewardingB. troublesomeC. expensiveD. labor-saving12. By saying “... the prophecy becomes self-fulfilling...” (Para. 2), the author means that __.A. girls will eventually find their goals in life beyond reachB. girls will be increasingly discontented with their life at homeC. girls will be capable of realizing their own dreamsD. girls will turn out to be less valuable than boys13. The author believes that a vicious circle can turn into a virtuous circle when _______.A. women care more about educationB. parents can afford their daughters’ educationC. girls can gain equal access to educationD. a family has fewer but healthier children14. What does the author say about women’s education?A. It has aroused the interest of a growing number of economists.B. It will yield greater returns than other known investments.C. It is now given top priority in many developing countries.D. It deserves greater attention than other social issues.15. The passage mainly discusses _______.A. unequal treatment of boys and girls in developing countriesB. the major contributions of educated women to societyC. the economic and social benefits of educating womenD. the potential earning power of well-educated womenPassage 4David Thomson is an electronics technician, trained by the U.S. Navy, who writes instruction books for complicated equipment. He believes that every person is surrounded by a force field that can broadcast emotions to other human beings. The ability to receive such fo rce fields, Thomson believes, explains how one can sense another’s fear, nervousness, aggression, panic, or friendliness.This theory of emotional communication occurred to Thomson when he told a psychiatrist, Dr. Jack Ward, that he was certain his own hypertension made those near him uncomfortable. To demonstrate the theory, Thomson constructed a transmitter capable ofgenerating an electromagnetic field similar to that of a man beset by hyper anxiety. For a year, with this in his pocket, Thomson made people miserable. He would find a hungry man delightedly preparing to eat a steak in a restaurant, turn on the transmitter, and watch as the man became tense and irritable and finally left with his steak uneaten. In another test, Thomson cleared a crowded room in fifteen minutes. Such an exodus could not be due, Thomson observed, to personality problems alone.Dr. Ward, who had become Thomson’s partner, insisted that there was already misery enough in the world. Thomson fashioned a “happiness transmitter,” which can duplicate the force field of a contented man. University psychologists in the United States report some encouraging results in current tests of the Thomson-and-Ward transmitter.The “happiness machine” has many possibilities. Thomson has speculated on its use near disturbed or anxious patients in hospitals, and in unruly crowds. Tranquility, like panic and violence, may be contagious.16. The theory is based on belief in the existence of______.A. complicated equipmentB. individual force fieldsC. nervousnessD. aggression17. The theory occurred to Thomson because he was convinced that people near him .A. could hypnotize himB. could make him feel uncomfortableC. were reading his thoughts D were affected by his hypertension18. For his first demonstrations, Thomson chose people who____.A. were in a happy moodB. seemed hyper anxiousC. were aggressiveD. Both B and C19. The Thomson-and-Ward transmitter was constructed because____.A. university psychologists suggested itB. the “misery machine” had not workedC. Dr. Ward felt there was misery enoughD. Police forces asked for it20. Thomson has speculated on_____.A. some helpful uses of a “happiness machine”B. possi ble wrongful uses of a “happiness machine”C. the disadvantages of a tranquil populationD. the final report on the psychologists’ testsPassage 5Does a bee know what is going on in its mind when it navigates its way to distant food sources and back to the hive, using polarized sunlight and the tiny magnet it carries as a navigational aid? Or is the bee just a machine, unable to do its mathematics and dance its language in any other way? To use Dondald Griffin’s term, does a bee have “awareness”, or to use a phrase I like better, can a bee think and imagine?There is an experiment for this, or at least an observation, made long ago by Karl von Firsch and more recently confirmed by James Gould in Princeton. Biologists who wish to study such things as bee navigation, language, and behavior in general have to train their bees to fly from the hive to one or another special place. To do this, they begin by placing a source of sugar very close to the hive so that the bees (considered by their trainers to be very dumb beasts) can learn what the game is about. Then, at regular interval, the dish or whatever is moved progressively farther and farther from the hive, in increments of about 25 percent at each move. Eventually, the target is being moved 100 feet or more at a jump, very far from the hive. Sooner or later, while this process is going on, the biologist shifting the dish of sugar will find the bees are out there waiting for them, precisely where the next position had been planned. This is an uncomfortable observation to make.21. The best title for the passage is_____A. Teaching the Bees to NavigateB. Testing the Awareness of BeesC. Navigational Techniques of BeesD. Behaviorists Versus Biologists: A Zoological Debate22. The word “awareness” in Paragrap h One appears in quotation marks in order to ____A. show the author’s preference for the termB. indicate that it is being used humorouslyC. acknowledge Donald Griffin’s previous use of the termD. point out that it was used differently earlier in the passage23. In the second paragraph Karl von Frisch is mentionedA. to introduce his observation on bee behaviorB. to contrast his theories with those of James GouldC. acknowledge Donald Griffin’s previous use of the termD. point out that it was used differently earlier in the passage24. According to the author, sugar was used in the study______A. to reward the bees for performing the experiment correctlyB. to train the bees to travel to a particular placeC. to ensure that the bees knew where the hive wasD. to ensure that the bees would obey the orders25. The result of the experiment explained in the passage seems to indicate that______A. research using bees is too dangerous to be conducted successfullyB. bees are unable to navigate beyond 100 feet their hiveC. scientists can teach bees to navigateD. bees are able to perform limited reasoning tasksPart II Vocabulary and Structure (0.5*40=20 points)Directions: There are 40 incomplete sentences in this part. For each sentence there are four choices marked A, B, C and D. Choose the ONE that best completes the sentence.1. If you lie once, people will think of you as a liar and interpret your remarks ______.A. certainlyB. accordinglyC. approximatelyD. appropriately2. The lightning flashed and thunder ______.A. bumpedB. struckC. collidedD. crashed3. Success in money-making is not always a good ______ of real success in life.A. essenceB. qualificationC. decreeD. criterion4. Because a circle has no beginning or end, the wedding ring is a symbol of ______ love.A. extravagantB. prominentC. eternalD. sincere5. This is a complete ______ for enforcing the new welfare regulations.A. legislationB. blueprintC. leaseD. penalty6. The policeman tried to ______ the teenage driver to obey the traffic laws rather than fine him directly.A. induceB. perplexC. indulgeD. lure7. He kept making ______ remarks instead of straight forward yes-or-no replies.A. opaqueB. ambiguousC. doubtfulD. oriental8. The managing director took the _____ for the accident, although it was not really his fault.A. guiltB. claimC. blameD. accusation9. There is something wrong with my TV set, I must have it ______.A. checkingB. checkC. to checkD. checked10. All flights ______ because of the storm, they decided to take the train.A. having cancelledB. were cancelledC. have been cancelledD. having been cancelled11. At last they succeeded ______ the job.A. to persuade him toB. in persuading him to takeC. to persuade him takingD. in persuading him taking12. The electric shaver ______ before it can be used.A. needs repairingB. requires to repairB. should be in repair D. has to be repairable13. You can fly to London this evening ______ you don’t mind changing planes in Paris.A. providedB. exceptC. unlessD. so far as14. The factory ______ next year will be one of the largest in this city.A. to buildB. to be builtC. being builtD. having been built15. Don’t say anything at the meeting unless ______.A. askingB. askedC. being askedD. to be asked16. There are several ______ leaves on the ground.A. fallingB. fallenC. to fallD. fell17. The price was very reasonable; I would gladly have paid ______ he asked.A. three times much asB. three times as many asC. as three times much asD. three times as much as18. We’d better wait ______, Peter and Tom will come very soon.A. a little longerB. more longerC. longD. as longer19. The doctors have tried ______ to save the life of the wounded soldier.A. everything possible humanlyB. humanly everything possibleC. everything humanly possibleD. humanly possible everything20. I was worried very muc h because I’ll miss my flight if the bus arrives ______.A. latelyB. lateC. latterD. more later21. It is ______ that I would like to go to the beach.A. so nice weatherB. such nice weatherC. so nice a weatherD. such a nice weather22. The reason why so many people sit before the television tonight is that there will be a______ show.A. livingB. liveC. aliveD. lived23. I ______ go to bed until I ______ finished my work.A. don’t/hadB. didn’t/haveC. didn’t/hadD. don’t/have24. The students in the classroom ______ not to make so much noise.A. needB. oughtC. mustD. dare25. The differences between ______ are gradually being eliminated.A. the town and the countryB. town and countryC. a town and a countryD. a town and the country26. We have produced ______ this year as we did in 1993.A. as much cotton twiceB. as twice much cottonC. much as twice cottonD. twice as much cotton27. ______ of the buildings were ruined.A. Three fourthB. Three fourC. Three-fourthsD. Three-four28. She went to the countryside ______.A. in the morning at nine / on June first, 1968B. on June first, 1968 / in the morning at nineC. at nine in the morning / on June first, 1968D. on June first, 1968 / at nine in the morning29. Three-fourths of the surface of the earth ______ covered with water.A. areB. isC. wereD. be30. The Olympic Games are held ______.A. every four yearsB. every four yearC. every fourth yearsD. every four-years31. ______, wherever he lives, a man belongs to some society.A. For shortB. In shortC. Of shortD. On short32. Tom has been sad recently, for his plan to go to college _____ at the last moment.A. fell outB. fell behindC. fell inD. fell through33. David likes country life and has decided to ______ farming.A. go in forB. go intoC. go throughD. go after34. Classroom testing, if well done, most certainly ___ a stimulus to study and real learning.A. acts forB. acts onC. acts asD. acts to35. The French pianist who had been praised very highly ____ to be a great disappointment.A. turned upB. turned inC. turned outD. turned down36. We regret to inform you that the materials you ordered are ______.A. out of workB. out of reachC. out of practiceD. out of stock37. A man who could ______ such treatment was a man of remarkable physical courage andmoral strength.A. bear uponB. insist onC. stand up toD. persist in38. Is his action consistent ______ his principles?A. withB. inC. ofD. by39. A foreign firm has bought more than half of the shares in his company and ______.A. got over itB. overtaken itC. taken it overD. overcome it40. Some animals will modify their behavior to ______ their environment.A. adapt toB. adopt toC. suit toD. conform toPart III Writing (30 points)Directions: For this part, you are to write a composition on the title of Sending Kids to Study Abroad.You should write at least 400 words and you should base your composition on the outline (given in Chinese) below.1.越来越多的家长把孩子送去国外读书2.这样做的好处和缺点3.我的观点。
山东科技大学708理论基础2017-2018年考研专业课真题试卷
一、名词解释(6小题,每题5分,共30分)
1、工艺美术运动
2、装饰艺术运动
3、解构主义
4、波普设计运动
5、米斯的少即是多
6、贝聿铭
二、简答题(3小题,每题10分,共30分)
1、何为系统设计?这种设计方法有什么益处?
2、试分析国际主义风格和现代主义设计风格的联系与区别?
3、包豪斯的历史作用及影响。
三、作品分析(在下面四个小题中自选2小题答题,每题20分,共40分)
1、图一是斯堪的纳维亚国家的设计作品,请做简要设计分析。
2、图二是约瑟夫·帕克斯顿的设计作品,请做简要设计分析。
3、图三是日本设计师福田繁雄的设计作品,请做简要设计分析。
4、图四是里特维斯的设计作品,请做简要设计分析。
图一 山东科技大学
2018年硕士研究生入学考试试题
考试科目:理论基础科目代码:708。
山东科技大学数学分析考研真题2017—2019年
2、证明:若 f (x) 在[a,b] 上连续,且 f (x) 0 ,则
ln 1
b f (x)dx 1
b
ln f (x)dx 。
ba a
ba a
五、定积分应用(共 15 分,第 1 题 7 分,第 2 题 8 分)
求由曲线 y x(1 x) 与 x 轴围成的区域 (1)绕 x 轴旋转一周所得旋
a
1 x
2、已知
x y
et et
cos t sin t
,求
d2y dx 2
。
三、计算下列积分(共 15 分,每题 5 分)
1、
e3x ex
1dx 1
,
2、 ln x 2dx ; x
n1
3、
1
ln[x]dx ,这里[x] 表
示不超过 x 最大整数。
四、证明不等式(共 15 分,第 1 题 7 分,第 2 题 8 分)
六、幂级数问题(共 12 分,第 1 题 8 分,第 2 题 4 分)
x
n 1
1、求幂级数
n1 n(n 1)
(1 x 1) 的和函数。
1
2、求级数
n1 n(n 1)2n
的值。
七、 多元函数的微分 (共 12 分) 已知函数
f
(x,
y)
x2y2
(x2
y2
3
)2
,
x2
y2
0
试证: f (x, y) 在 (0,0) 处连续且存在偏导数,
x2 y2 2z
z2
, 从 z 轴正向看去,取逆时针方向。
十一、曲面积分(共 12 分)计算第二型曲面积分
山东科技大学2009年数学专业考研数学分析真题
一.求极限(20分):1、曲线)(x f y =与x y sin =在原点相切,证明:2)2(lim =∞→nnf n 。
2、求极限:⎪⎭⎫⎝⎛-→x x x x cot 11lim 0。
3、求520)]cos(1[limxdtt x x ⎰-+→。
4、求极限⎪⎪⎭⎫⎝⎛++++++∞→32323212111lim n n n n n n nn 。
二.导数及高阶导数(20分):1、设35x x x y ++=,求'y 。
2、已知xx y -=14,求)4()(>n yn 。
3、由方程⎰-=+x y dt t y x 022)cos(确定了y 是x 的函数,求dxdy 。
4、设)()('),('t f t tf y t f x -==,)('''t f 存在且)(''t f 不为零,求三阶导数33dxyd 。
三.证明题(17分):1、设)(x f 在)0(],[>a b a 上连续,在),(b a 内可导。
证明:存在),(,b a ∈ηξ 使)('2)('ηηξf ba f +=。
2、证明:方程)2(11≥=+++-n x xx n n在)1,0(内必有惟一实根n x ,并求n n x ∞→lim 。
四.积分计算(18分):1、计算不定积分:⎰+2)1(x e dx。
2、计算定积分:dx e x ⎰-2ln 01。
3、讨论反常积分)0()1)(1(02>++⎰∞+ααx x dx的敛散性,若收敛,求出其值。
五. 解下列各题(30分)1、设22()z f x y =+ , 其中f 具有二阶导数, 求22zx∂∂, 2z x y ∂∂∂。
2、计算积分 (),lx y ds +⎰:l 顶点为(0,0), (1,0), (1,1)的三角形边界。
3、计算积分xdydz ydzdx zdxdy ∑++⎰⎰,∑为锥面22y x z +=在平面4=z 下方的部分,取外法线方向。
2016年山东科技大学考研真题811地理信息系统硕士研究生专业课考试试题
山东科技大学2016年全国硕士研究生招生考试
地理信息系统试卷
一、概念题(每题5分,共30分)
1、地理信息
2、元数据
3、地理空间索引
4、图层
5、空间信息可视化
6、空间数据引擎
二、单选或多选题(每题5分,共30分)
1、 GIS内部数据结构基本上分为两大类,这两大类是指()
A.物理结构和几何结构
B. 矢量结构和栅格结构
C. 逻辑结构和物理结构
D. 实体结构和要素结构
2、下面常用GIS软件中非国产软件为()
A. MapInfo
B. GeoStar
C. MapGIS
D. SuperMap
3、在“3S”系统中具有数据管理功能的系统为()
A. GPS
B. RS
C. GPRS
D. GIS
4、空间分析的网络分析中,网络数据结构的基本组成部分为()
A. 区域 (Polygon)
B. 链(Link)
C. 节点(Node)
D. 文字(Text)
5、GIS中地理要素通常抽象为下面哪几种几何要素()
A. 点
B. 线(或弧)
C. 多边形(或区域)
D. 三角形
6、下列哪一个是数字高程模型的缩写.( )
A. DTM
B. DEM
C. EDM
D. PDA。
山东科技大学2011-2016年招收硕士学位研究生入学考试电路试卷
山东科技大学2011-2016年招收硕士学位研究生入学考试电路试卷山东科技大学2011年招收硕士学位研究生入学考试电路试卷山东科技大学2012年招收硕士学位研究生入学考试电路试卷一、单项选择题:(本大题共10小题,每小题4分,总计40分)在下列各题中,有四个备选答案,请将其中唯一正确的答案写到答题纸上,不要写在试卷上!1.图示二端电路中与理想电压源并联的电阻RA. 对端口电压有影响B. 对端口电流有影响C. 对端口电压与端口电流均有影响D. 对U支路的电流有影响S(答案必须写到答题纸上)2.图所示电路中0N 为无源线性电阻网络,当S U =0,S 4I =A 时,26U =V ;当S U =8 V 时,电流源S I 不吸收也不产生功率;则当S U = 12 V 时,电流源吸收的功率应为A. 16 WB. 14 WC. 12 WD. 10 W(答案必须写到答题纸上)3. 图示正弦交流电路,角频率1rad/s ω=时,(复)阻抗Z 为 A.(2j2)+ΩB.(2j2)-Ω45Ω°45-Ω°(答案必须写到答题纸上)4. 某负载所取的功率为72kW ,功率因数为0.75(电感性,滞后),则其视在功率为 A.72kVB.81.6kVAC.96kVAD. 54kVA(答案必须写到答题纸上)5.RLC 串联谐振电路的电感增至原来的4倍时,谐振频率应为原来的A.12倍B.2倍C.4倍D.14倍 (答案必须写到答题纸上)6.若20∶1理想降压变压器的次级线圈中0.6Ω电阻的电压为6V ,则该变压器的次级电流和初级电流为 A. 10A ,5A B. 5A ,10A C. 10A ,0.5A D. 0.5A ,10A(答案必须写到答题纸上)7. 如图示正弦全波整流波形i 的有效值为10A ,半波整流波形i 1的有效值为A.102AC. A D. 104A(答案必须写到答题纸上)8.如图所示电路零输入响应的性质为 A. 过阻尼 B. 临界阻尼 C. 欠阻尼 D. 无阻尼(答案必须写到答题纸上)9.二端口网络Y 参数中,y 22是二端口的 A. 输出端导纳B. 输入端开路时的出端导纳 C. 输入端短路时的转移导纳D. 以上皆非(答案必须写到答题纸上)10.某电阻电路仅含一个独立电压源,其电压为S ()u t ,若已知其中某条支路的电流2S S ()0.5()0.2()i t u t u t ⎡⎤=+⎣⎦A ;则此电路属于A. 线性、时不变电路B. 非线性、时不变电路C. 线性、时变电路D. 非线性、时变电路(答案必须写到答题纸上)二、(20分)电路如图T2所示,试写出节点方程并求其节点电压及i 1、i 2。
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2、求幂级数
1 2 x 2 3x2 3 4 x3 n (n 1) xn
的收敛域以及和函数。
3、证明含参变量反常积分 exydy 在[a, b](a 0) 上一致收敛。 0
八、(6分)证明函数项级数
n 1
1 nx
在 (1, ) 上有连续的各阶导函数。
在,但在 0, 0 点处不可微。
2、设函数 u f (x, y, z) 有连续的一阶偏导数,又函数 y y(x) 和 z z(x) 分
别由 exy y 2, ex zx sin t dt 确定,求 du .
0t
dx
3、在曲线 x2 y2 1上找一个位于第一象限的点,使得该曲线在该点处的 4
1、计算定积分 2 sin5x cos x dx . 0
2、计算不定积分
1 4 sin2 x cos2 x dx
.
3、设函数 f (x) 在区间[0,1] 上可积,且满足 arctan x f ( x) 1 f ( x)dx, 求 0 1 f (x)dx 的值。 0
4、函数 f (x) 在区间[a, a] (a 0) 上连续,证明
a f (x)dx 1 a f (x) f (x)dx ,
a
2 a
并求定积分 1 x4 dx 的值。 11 ex
四、一元微分学 (每题8分,共16分)
1、函数 f (x) 在[a, b] 上连续,在 (a,b) 上可微,证明:存在 (a,b),使下 式成立
2 f (b) f (a) b2 a2 f '( ).
山东科技大学2016年招生硕士学位研究生入学考试试卷
一、极限及其应用(每题6分,共18分)
1、 计算
lim
n
1
2
n
2
n
.
2、 计算
lim
1
1
1
.
n n2 1 n2 2
n2 n
3、计算 lim tan x sin x . x0 ln(1 x3 )
切线与该曲线以及 x 轴、 y 轴所围成的图形面积最小,并求最小面积。
六、多元函数积分学(每题8分,共16分)
1 、 计 算 三 重 积 分 (x z)dxdydz , 其 中 V 是 由 z x2 y2 与 V z 1 x2 y2 所围成的区域。
2、计算 2x3dydz 2 y3dzdx 3(z2 1)dxdy ,其中 S 是曲面 z 1 x2 y2 S 在 z 0 部分并取上侧。
七、级数和含参量积分(第1,2小题各9分,第3小题7分,共25 分)
1、已知正项级数 un , n 1
(1)证明:当 un 收敛时,级数 unun1 也收敛。
n 1
n 1
(2)若级数 unun1 收敛,判断级数 un 是否收敛?若收敛,请
n 1
n 1
Hale Waihona Puke 给与证明;若发散,请举例说明。二、 导数与微分(每题6分,共18分)
1、求由参数方程
x y
a(t a(1
sin t) cos t)
所确定的函数的导数
dy dx
与
d2y dx2
.
2、已知函数 y xsin x ,求 dy . dx
3、求函数 y 1 的 n 阶导数。 x(1 x)
三、积分及其应用(每题6分,共24分)
2、设函数 f (x) 在[a, ) 上连续,且 lim f (x) 存在,证明 f (x) 在[a, ) 上 x 一致连续。
五、多元微分学(每题9分,共27分)
1、证明函数
f
(x,
y)
x2 y
x2
y2
,
x2 y2 0
0,
x2 y2 0
在点 0, 0 处连续且偏导数存