南昌大学 2013～2014学年第一学期期末考试试卷
2013-2014-1工程力学I试卷(A)
D、 30 3kN 。
图3
图4 ） 。
4、 如图 4 所示刚体受力偶 （F， F′） 和在该力偶作用面内的力 P 作用而平衡， 这是由于 （ A、约束反力与力偶（F，F′）平衡； C、P 与约束反力构成的力偶与力偶（F，F′）平衡；
B、P 与力偶（F，F′）平衡； D、P 与约束反力平衡。
5、在一般情况下，平面任意力系向作用面内任一点简化，得到主矢和主矩，其中主矩与简化 中心的位置（ A、有关； ） B、无关； C、关系不大； D、不能确定。
第 5 页
共 7 页
得 分 五、计算题：（15 分）
评阅人
槽形截面悬臂梁，受力和尺寸如图所示，F＝40kN，M＝60kN·m。已知截面对形心轴 z 的 惯性矩 Iz＝1.017×108mm4，形心坐标 yC＝96.4mm，材料的许用拉应力 t ＝60MPa，许用压 应力 c ＝160MPa。（1）画出图示梁的剪力图和弯矩图；（2）校核梁的正应力强度。
B、力系可简化为一个合力； D、力系可简化为合力和合力偶矩。
3、如图 3 所示均质圆球放在光滑的斜面上，斜面的倾角为 30 0 ，圆球重 P=10kN，受一与 斜面平行的拉力 FT 作用而平衡，则斜面对圆球的约束反力的大小为（ A、 5 3kN ； B、 10 3kN ； C、 20 3kN ； ）。
图5 7、螺钉受拉力作用，如图 6 所示，则剪切面积应取为（ A、 A ）
图6
d 2
4
；
B、 A d ；
2
C、 A dh ；
D、 A
d 2
2
。 ）
8、如图 7 所示空心圆轴扭转时，受扭矩 T 作用，其横截面切应力分布的正确表达应为（
南昌大学期未试卷格式
南昌大学 2011～2012 学年第一学期期末考试试卷试卷编号：6031 ( C )卷课程编号：J5502Z007 课程名称：普通物理（光学）考试形式：闭卷适用班级：10物理学、10应物姓名：学号：班级学院：专业：考试日期：题号一二三四五六七八九十总分累分人签名题分40 30 30 100得分考生注意事项：1、本试卷共5页，请查看试卷中是否有缺页或破损。
如有立即举手报告以便更换。
2、考试结束后，考生不得将试卷、答题纸和草稿纸带出考场。
一、填空题：(每空2分，共 40分)得分评阅人1、光强均为I o的两束相干光相遇而发生干涉时，在相遇区域内有可能出现的最大光强是__________。
2、当一束自然光在两种介质分界面处发生反射和折射时，若反射光为完全偏振光。
则折射光为_________偏振光，且反射光和折射光之间的夹角为___________。
3、光的偏振现象说明光波是_________波。
4、用纳光灯的纳黄光垂直照射光栅常数为d =3μm的衍射光栅，第五级谱线中纳黄光的(589.3nm)的角位置Φ5 = 。
5、在空气中用波长为λ的单色光进行双缝干涉实验时，观测到干涉条纹相邻明条纹的间距为1.33mm，当把实验装置放在水中时（水的折射率n=1.33），则相邻明条纹间距变为____________________。
6、若出射的同心光束是会聚的我们称之为__________。
7、把折射率为1.5 的玻璃片插入杨氏实验的一束光路中,光屏上原来第5 级亮条纹所在的位置为中央亮条纹，插入的玻璃片的厚度为_________。
(已知光波长为6×10-7m.)8、在双折射晶体内部，光在晶体内沿______传播时，e光和o光的传播速度相等。
9、若波长为6250 Ǻ的单色光垂直入射到一个每毫米有800条刻线的光栅上时，则该光栅的光栅常数为；第一级谱线的衍射角为。
10、人眼的明视距离cm。
11、物镜直径D=5cm的望远镜对可见光平均波长λ＝550nm的最小分辨角是_______。
2013-2014学年度第一学期 (7)
子制造的材料。
13. 基因表达就是遗传信息表现为生物性状的过程。
14. 计算机语言就是一套计算机能识别的指令系统。
四、简答题(每题 15 分，共 30 分)
15. 爱因斯坦在关于狭义相对论的第二篇短文中论述了质量与能量的关系
6E=(6m)c2
式中 E 为能量 ， m 为质量， c 为光速。光的速度为 c=3X10 8 km/s ，是一切物质运动速度
提出了"可持续发展"的概念:人类应当享有与自然和谐的方式，过健康而富有生产成果的生活 权利，既满足当代人的需求，也不损害、削弱子孙后代满足其自身需求的能力。可持续发展是 指社会、经济、人口、资源和环境的协调以及长期延续的发展，它是一种健康的、公正的发展。
(1 0 分) (2) 其中心思想可以表述如下: 可持续发展的核心是"发展"，这种发展应是不断满足当代人和后代人的生产、生活和发 展，以及他们对于物质、能量、信息和文化的需求。 可持续发展的重点是"公平"，这种公平体现在代际之间用公平的原则，去使用和管理属于 全人类的资源和环境，每代人都要以公正的原则担负起各自的责任，当代人的发展不能以牺牲 后代人的发展为代价。 可持续发展的关键是"合作"，在国际社会和地区际之间应体现均富、合作、平等的原则，在 空间范围内，缩短同代人之间的差距，不应造成物质上、能量上、信息上乃至心理上的鸿沟，以 实现"资源←生产一市场"内部之间的协调和统一。 可持续发展的本质是"协调"。人类社会要营造"自然一社会 经济"支持系统适宜的外部 条件，使得人类生活在一种更严格、更有序、更健康、更愉悦的环境之中。(1 0 分) (3) 可结合近几年频发的自然灾害，谈谈自己的感想。(1 0 分)
江西省南昌市2013-2014学年高一上学期期末终结考试化学试题(扫描版,答案文档版).pdf
2013—2014学年度第一学期南昌市期末终结性测试卷
高一化学(甲卷)参考答案及评分意见
第Ⅰ卷（共48分）
一、选择题（每小题只有一个正确答案，请将正确答案填入表格中。
每小题3分，共48分。
）
12345678910111213141516DBCACADADCBDCCCB第Ⅱ卷（共52分）
二、填空简答题（共27分）
17. （9分）（1）过滤（2）Al2O3； Fe2O3；K2SO4和（NH4）2SO4
（3）①Al2O3＋2OH＝2AlO2＋H2O
②Al3+＋3NH3·H2O＝Al(OH) 3↓＋3NH4+
18．（分）2Fe(OH)3 △Fe2O3 + 3H2O（2分）
(3) 2Fe3++Fe＝
19. （12分）（1）d e
（2）FeCl32Fe3++Fe＝3Fe2+ ，防止Fe2+被氧化
用试管取少量C溶液，滴加KSCN溶液，无颜色变化，再滴加氯水（或硝酸），溶液呈血红色，证明原溶液中有Fe2+存在. （12分）（1）②；白色固体变蓝色；带火星；复燃。
（2）未反应的二氧化碳与石灰水反应所致。
（3）由于生成氧气的量减少，E中可能会因二氧化碳与石灰水反应而倒吸。
（4）小；30；Na2O2可能含有其它杂质D装置可能有氧气未被排出。
四、计算题（共13分）
21．(分) (1)1 (2)20（1分） (3)1(4)200（3分）
22．（分）
：
：。
13级《高等数学I、II》(上)期末考试卷及答案
2013—2014学年第一学期《高等数学I 、II 》考试试卷（A 卷）一、填空题（每小题3分，共48分）1. 2()ln(1)f x x =-, 已知 000()(2)3lim2h f x f x h h →--=, =0x 13- .2. 2sin 10()0ax x e x f x x a x ⎧+-≠⎪=⎨⎪=⎩在0x =处连续，则a = 1- . 3. 函数32()391f x x x x =--+的既递减又上凸的区间是 (1,1)- .4. 21tx t y e ⎧=+⎨=⎩，则22d d y x 4t t． 5. 设)(x f 在0=x 点处连续，且0()lim12x f x x→=，那么(0)f '= 2 6. 222||2x x dx x -++⎰ ln3 .7.x y dye dx+=的通解为 y x e e c --=+ 8. 设3(1)f x x +=，则(1)f x '-= 23(2)x - ．9. 方程2610y e xy x ++-=确定隐函数()y y x =，则(0)y '= 0 。
10. 若函数)(x f 具有二阶连续导数，,0)()(21='='x f x f ),(0)( 21x f x f ''<<''则12(),().f x f x 的大小关系为 ).()(21x f x f >11. 变上限函数⎰21sin x tdt 的导数等于 2sin 2x x12. 设x ，x e ，x e -是二阶非齐次线性微分方程)()()(x f y x b y x a y =+'+''的三个特解，则该方程的通解为x x e C x e C y x x +-+-=-)()(21。
得 分13. 广义积分21(ln )edx x x +∞⎰= 1 。
14. 微分方程052=+'-''y y y 的通解为12(cos 2sin 2)x y e c x c x =+ 15. ⎰⎰'+=dx x f x c x dx x f )( ,sin )(2 2sin 2sin x x x C -+ .16. 函数x e x f -=)(的四阶麦克劳林公式是)(!!!443243211x o xx x x ++-+-二、计算题（满分24分，每小题6分）17.求020()lim (0,0)ln(1)xt t xx a b dt a b t dt→->>+⎰⎰)(b a ≠原式=-+→limln()x x x a b x 0212 3分=-+→lim ln ln x x x a a b b x 0412=14lna b 3分18、求曲线xex y 12-+=)(的渐近线。
2013-2014学年第一学期期末考试试题 2
考前注意事项：●试卷统一用A4纸双面打印后提交给各班班长●试题中的题录保存统一按以下标准格式著录:1.期刊论文格式主要责任者.文献题名［J］。
刊名，出版年份,卷号(期号)：起止页码．如：褚婷婷.世界经济亟需一个再平衡过程［J].两岸关系，2005,（4）：32-33.2.学位论文格式主要责任者．文献题名[Ｄ］．保存地：保存单位，年份如：张和生．地质力学系统理论［Ｄ］．太原：太原理工大学,1998。
3. 图书格式主要责任者．书名［M］．出版地：出版者,出版年如：刘国钧，郑如斯．中国书的故事[M］。
北京:中国青年出版社,1979.●拷贝屏幕的操作如下：CTRL+ALT+A三键进行截屏,在题目结尾处点击鼠标右键粘帖界面即可。
屏幕图可适当缩小.海南大学2013-2014学年第一学期《文献信息检索与利用》试卷学号 20121714310090姓名张方石学院经济与管理学院年级大二专业金融学任课老师李春香成绩一、在计算机检索系统中，布尔逻辑符有几个？写出中文和英文的布尔逻辑符号，以及所表达的关系；检索效果评价有哪两个最重要的指标？（10分）答：布尔逻辑符有三种。
分别是“与”、“或”、“非"，分别用“and”、“or”、“not”来表示,也可以用“＊”、“+”、“—”来表示.下面用检索词A和检索词B来表达之间的关系.逻辑“与”用“AND”或“＊"表示。
可用来表示其所连接的两个检索项的交叉部分,也即交集部分。
如果用AND连接检索词A和检索词B,则检索式为：A AND B （或 A*B）:表示让系统检索同时包含检索词A和检索词B的信息集合C。
逻辑“或"用“OR"或“+"表示.用于连接并列关系的检索词。
用OR连接检索词A和检索词B,则检索式为:A OR B（或 A＋B）.表示让系统查找含有检索词A、B之一，或同时包括检索词A和检索词B的信息。
逻辑“非”用“NOT”或“-"号表示.用于连接排除关系的检索词,即排除不需要的和影响检索结果的概念.用NOT连接检索词A和检索词B，检索式为:A NOTB （或A—B).表示检索含有检索词A而不含检索词B的信息，即将包含检索词B 的信息集合排除掉.检索效果评价有哪两个最重要的指标是查全率和查准率.查全率=检索到的文献/数据库中所有文献＊100％。
20132014学年度第一学期南昌市期末终结性测
2013—2014学年度第一学期南昌市期末终结性测试卷八年级(初二)英语听力材料、参考答案及评分意见Ⅰ．听力材料：A）请听下面10段对话，从A、B、C三个选项中选出最佳选项，每段对话读两遍。
1. W: What do you want to be when you finish high school, Tom?M: Well, my parents want me to be a doctor, but I want to be a pilot.2. M: I think books will be on computers, not on paper.W: I agree.3. M: Do you like butter? I want to put some butter in the sandwiches.W: Sorry, I can’t stand it. I like lettuce very much.4. M: Can you make fruit salad, Ann?W: Yes. And my sister can make it, too. My mother taught us to do it last year.5. W: Eric, can you go to the mall with me this weekend?M: Sure, I’d love to. What do you want to buy?W: Some food and drinks.6. W: Do you want to go and see a movie with me, Tina?M: I am afraid I can’t. I’ll have to help mom with some washing.7. W: I’ll bring some snacks to the classroom tomorrow.M: You’d better not. If you do, our teacher will be angry.W: OK. I’ll bring some magazines instead.8. W: What’s the time by your watch, Dad?M: A quarter past seven.W: Oh, it is time to watch basketball match on CCTV5.9. W: Where do you live, Peter?M: I live on a farm. I think the farm life is better than the city life. What about you, Jane?W: I don’t agree. The city life is more interesting.10. W: Mother’s Day is coming. What should I get for my mother?M: I think flowers are the best choice. I believe she’ll like them.W: Yeah, I think so. Thank you!B）请听下面3段对话，听完对话后从A、B、C三个选项中选出最佳选项，每段对话读两遍。
南昌大学2013-2014学年第一学期研究生英语试卷
the auspices The mortalityyears down the road.a plungeidentifiableless pronouncedfor immersionapparelsingle punditthe pivotalquery aerial cognition expression attest robotics meld cover vital arise guideline deploy recapitulate endow collection In the journal Science, Professor Sharkey calls for ethical guidelines to (1)_______ all aspects of robotic technology, not just in the home and workplace, but also on the battelfield, where lethal robots such as the missile-armed Predator drones used in Iraq and Afghanistan are already (2) _______ with lethal effect. The US Future Combat Systems project aims to use robots as “force multipliers”, with a single soldier initiating large-scale ground and (3)_______ attacks by a robot droid army. “Robots for care and for war represent just two of many ethically problematic areas that will soon (4)________ from the rapid increase and spreading diversity of robotics applications, ” Professor Sharkey said, “Scientists and engineers working in robotics must be mindful of the potential dangers of their work, and public and international discussion is (5)_____ in order to set policy guidelines for ethical and safe application beford the guidelines set themselves.” The call for controls over robots goes back to the 1940s when the science-fiction author Isaac Asimov drew up his famous three laws of (6)_______. The first rule stated that robots must not harm people; the second that they must obey the commands of people provided they does not conflict with the first law; and the third law was that robots must attempt to avoid harming themselves provided this was not in conflict with the two other laws. Asimov wrote a (7)______ of science fiction sories called I, Robot which exploited the issue of machines and morality. He wanted to counter the long history of fictional accounts of dangerous automatons --- from the Jewish Golem to Mary Shelly’s Frankenstein --- and used his three laws as a literary device to exploit the ethical issues arising from the human interaction with non-human, intelligent beings. But late 20th –century prdictions about the rise of machines (8) ______ with superior artificial intelligence have not been realized, although robot scientists have given their mechanical proteges (门客准智能的) traits such as simple speech 门客) quasi-intelligent (准智能的recognition, emotional (9) ________ and face recognition. Professor Starkey believe that even dumb robots need to be controlled. “I’m not suggesting like Asimov to put ethical rules into robots, but to just to have (10)______ on how robots are used, ” he said. “Current robots are not bright enough even to be called stupid. If I even thought they would be superior in intelligence, I would not have these concerns. They are dumb machines not much brighter thatn the average washing machine, and that’s the problem.” Part II: Reading comprehension ( 20%) In this part, you will read four passages. You are required to choose the best answer to each question according to the passage and then mark your answer on the Answer Sheet by blacking the letter in the brackets. Passage OneArchaeology（考古学） is a source of history, not just a humble auxiliary discipline. Archaeological data are historical documents in their own right, not mere illustrations to written texts. Just as much as any other historian, an archaeologist studies and tries to reconstitute the process that has created the human world in which we live—and us ourselves in so far as we are each creatures of our age and social environment. Archaeological data are all changed in the material world resulting from human action or ,more succinctly, the fossilized results of human behavior. The sum total of these constitute what may be called the archaeological record. This record exhibits peculiarities and deficiencies the consequences of which produce a rather superficial contract between archaeological history and the more familiar kind based upon written records.Not all human behavior fossilizes. The words I utter and you hear as vibrations in the air are certainly human changes in the material world and may be of great historical significance. Yet they leave no sort of trace in the archaeological records unless they are captured by a Dictaphone or written down by a clerk. The movementof troops on the battlefield may “change the course of history,” but this is equally ephemeral from the archaeologist’s standpoint. What is perhaps worse, most organic material are perishable . Everything made of wood, hide, wool, linen, grass, hair, and similar materials will decay and vanish in dust in a few years or centuries, save under very exceptional conditions. In a relatively brief period the archaeological record is reduced to more scraps of stone, bone, glass, metal, and earthenware. Still modern archaeology, by applying appropriate techniques and comparative methods, aided by a few lucky finds from peat bogs deserts, and frozen soil is able to fill up a good deal of the gap.1.What is the author’s main purpose in the passage?A．To point out the importance of recent advances in archaeology.B．To describe an archaeologist’s education.C．To explain how archaeology is a source of history.D．To encourage more people to become archaeologists.2. The word “succinctly” in line 6 is closest in meaning to___A．concisely. B．briefly. C．clearly. D．appropriately.3. According to the passage, the archaeological record consists of ____A．spoken words of great historical significance.B．the fossilized results if human activity.materialsorganic materialsC．organicD．ephemeralideas.4. Which of the following is NOT mentioned as an example of an organic material?A．stone. B．wool. C．grass. D．hair.5. The paragraph following the passage most probably discusses_____A．techniques for recording oral histories.B．certain battlefield excavation methods.C．some specific archaeological discoveries.D．building materials of the nineteenth and twentieth centuries.Passage TwoThe modern age is age of electricity. People are so used to electric lights, radio, televisions, and telephones that it is hard to imagine what life would be like without them. When there is a power failure, people grope about in flickering candlelight, cars hesitate in the streets because there are no traffic light to guide them, and food spoils in silent refrigerators.Yet, people began to understand how electricity works only a little more thantwo centuries ago, Nature has apparently been experimenting in this field for millions of years. Scientists are discovering more and more that the living world may hold many interesting secrets of electricity that could benefit humanity.All living cells send out tiny pulses of electricity. As the heart beats, it sends out pulses of recorded, they form an electroencephalogram , which a doctor can study to determine how well the heart is working. The brain, too, sends out brain waves of electricity, which can be recorded in an electroencephalogram. The electric currents generated by most living cells are extremely small-often so mall that sensitiveinstruments are needed to record them. But in some animals, certain muscle cells have become so specialized as electrical generators that they do not work as muscle cells at all. When large numbers of these cells are linked together, the effects can beastonishing.The electric eel is an amazing storage battery. It can send a jolt of as much as eight hundred volts of electricity through the water in which it lives (An electric house current is only one hundred twenty volts). As many as four-fifth of all the cells in the electric eel’s body are specialized for generating electricity, and the strength of the shock it can deliver corresponds roughly to the length of its body.1. What is the main idea of the passage?A. Electric eels are potentially dangerous.B. Biology and electricity appear to be closely related.C. People would be at a loss without electricity.D. Scientists still have much to discover about electricity.2. The phrase “grope about” inline 3 could best be replaced by______.A. A. feel feel feel aboutB. about B. move move move aboutC. about C. flickerD. flicker D. run run run away away3. The author mentions all of the following as results of a blackout EXCEPT_____.A. refrigerated food items may go bad.B. traffic light do not work.C. people must rely on candlelight.D. elevators and escalators do not function.4. Why does the author mention electric eels?A. To warn the reader to stay away from them.B. To compare their voltage to that used in houses.C. To give an example of a living electrical generator.D. To describe a new source of electrical power.5. It can be inferred from the passage that the longer an eel is the ______. A. more beneficial it will be to scienceB. more powerful will be its electrical chargeC. easier it will be to fidD. tougher it will be to eatPassage ThreeThe difference between a liquid and a gas is obvious under the conditions oftemperature and pressure commonly found at the surface of the Earth. A liquid can be kept in an open container and fills it to the level of a free surface. A gas forms no free surface but tends to diffuse throughout the space available, it must therefore be kept in a closed container or held by a gravitational field, as in the case of a planet’satmosphere. The distinction was a prominent feature of early theories describing the phase of matter. In the nineteenth century , for example ， one theory maintained that a liquid could be “dissolved” in a vapor without losing its identity, and another theory held that the two phases are made up of different kids of molecules: liquidond and gasons. The theories now prevailing take a quite different approach by emphasizing what liquids and gases have in common. They are both forms of matter that have no permanent structure and they both flow readily. They are fluids.The fundamental similarity of liquids and gases becomes clearly apparent when the temperature and pressure are raised somewhat. Suppose a closed containerpartially filled with a liquid is heated .The liquid expands, or in other words becomes less dense as the evaporated molecules are added to it. The combination oftemperature and pressure at which the densities become equal is called the critical point. Above the critical point the liquid and the gas can no longer be distinguished; there is single, undifferentiated fluid phase of uniform density.1. According to the passage ,the difference between a liquid and a gas under normal conditions on Earth is that the liquid______.A. is affected by changes in pressureB. has a permanent structureC. C. forms forms forms a a a free free free surfaceD. surface D. is is is considerably considerably considerably more more more common common2. It can be inferred from the passage that the gases of the Earth’s atmosphere are contained by_________.A. A. a a a closed closed closed surfaceB. surface B. the the the gravity gravity gravity of of of the the the planet planetC. C. the the the field field field of of of spaceD. space D. its its its critical critical critical point point3. According to the passage, in the nineteenth century some scientists viewed liquidons and gasons as ________.A. A. fluidsB. fluids B. dissolving dissolving dissolving particles particlesC. heavy moleculesD. different types of molecules4. According to the passage , what happened when the temperature is increased in a closed container holding a liquid?a. the liquid and gas phases become more similar.b. the liquid and the gas become less dense.c. the container expands.d. the liquid evaporates out of the container.5. According to the passage, which of the following is the best definition of the critical point?a. when the temperature and the pressure are raised除草劑：巴斯德通过大量科学实验证明，如果生奶加工时温度超过℃，℃， 则其中的营养物质和生物活性物质会被大量破坏，但如果低于℃时，则其营养物质和生活活性物质被保留，并且有害菌大部分被杀灭，有些有益菌却被存留。
2013-2014南昌大学大一第一学期高数考试试卷及答案
一、单项选择题（每题3分，共15分）1.设对任意x ，总有ϕ(x )≤f (x )≤g (x )，且0)]()([lim =-∞→x x g x ϕ，则)(lim x f x ∞→ ( )A.存在且等于零B.存在但不一定等于零C.一定不存在D.不一定存在 2. x =0是函数xx x f 1sin )(=的( )A.可去间断点B.跳跃间断点C.无穷间断点D.振荡间断点 3.下列函数的弹性函数不为常数的为( )，其中a , b , α为常数 A. y =ax +b B. y =ax C.xa y = D. y =x α 4.若函数f (x )在点x 可微，则当∆x →0时，∆y -dy 较之dy 为( )无穷小A.同阶B.等价C.低阶D.高阶 5.设f (x )在区间[a , b ]上连续，则dt t f x F xa ⎰=)()(在区间[a ,b ]上( ) A.不一定有界 B.不一定连续 C.不一定可积 D.一定可导 二、填空题（每空3分，共15分）1.若函数f (x )的定义域为D =]4,0[π，则f (arcsin x )的定义域为__________2.=-+∞→}ln )2[ln({limn n n n __________ 3.若⎩⎨⎧≥+<=0,0,)(x bx a x e x f x 在x =0处可导，则b =_________4.设函数f (x )在(-∞,+∞)上连续，则])([dx x f d ⎰=__________5.dx x x ⎰--+1122)1(=__________三、求下列极限（每题6分，共12分）1.求极限1cos 1)1(lim3120--+→x x x 2.求极限)tan (sec lim 2x x x -→π 四、求下列各题（每题6分，共12分） 1.设y =(ln x )x ，求y '2.求由参数方程⎪⎩⎪⎨⎧-==ty t x 1212所确定的函数的二阶导数22dx y d五、求下列不定积分（每题6分，共12分） 1.dx x⎰+11 2.dx xx⎰2ln 六、求下列定积分（每题6分，共12分） 1.dx x x ⎰-π03sin sin 2.dx x ⎰51ln 七、应用题（每题8分，共16分）1.某产品的总成本C （万元）的边际成本为生产量x （百台）的函数C '(x )=1，总收益R （万元）的边际收益为生产量x （百台）的函数R '(x )=6-x ，（1）求生产量等于多少时，总利润最大？（2）从利润最大的生产量又生产了100台，总利润减少了多少？2.求由抛物线y +1=x 2与直线y =1+x 所围图形的面积。
江西省南昌市2013-2014学年高一上学期期末终结考试数学试题(扫描版,答案文档版).pdf
2013—2014学年度第一学期南昌市期末终结性测试卷 高一数学(甲卷)参考答案及评分意见 选择题（本大题共10小题，每小题3分，共30分） 答案CBBAACCABD填空题（本大题共5小题，每小题4分，共20分，请将正确答案填写在横线上） 11. ； 12．3； 13. 0； 14. ； 15．或 三、解答题（本大题共5小题，共50分．解答应写出文字说明、证明过程或演算步骤） 1．原式=……………………………………………………4分 ……………………………………………………………………8分 17．解：(1)由题意知，当燕子静止时，它的速度为0，代入题目所给公式可得 0＝5log2，解得Q＝10， 即燕子静止时的耗氧量为10个单位．…………………………5分 (2)将耗氧量Q＝80代入公式得 v＝5log2＝5log28＝15(m/s)，…………………………9分 即当一只燕子耗氧量为80个单位时，它的飞行速度为15m/s. ……………………………10分 18．解：（1）从图知，函数的最大值为1，则A=1．………………………………………1分 函数f（x）的周期为．所以=2………………………………………2分 又时，所以 而，则，…………3分 ∴函数f（x）的表达式为． ………………………………………………5分（2）由，得即………………………………………………………………………………6分 ∴∴………………………………………8分 ∵＞0，为△ABC的内角， ∴sin＞0，cos＞0，即＞0．∴．………………………10分 19. 解：（1）………3分 ∴ ………………………………………………………………………5分 （2）由（1）知 ∴ …………………6分 ∵，∴ ∵ …………………7分 ∴ ∴ ……………………………………………8分 ∴………10分 20.解：（1）若时， ……3分 则，此时的； ………………………………………5分（2）证明：………6分 令，记 …………………7分 则其对称轴 当，即时， ………………………………………9分 当，即时， ………………………………………11分 故 ……………………………………12分。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
南昌大学 2013～2014学年第一学期期末考试试卷一、 填空题(每空 3 分，共 15 分)1.函数1()lg(3)f x x =+- 的定义域是 。
2. 设函数y arctan = 则dy = 。
3. 函数3(1)(1)y x x =-+的单调增加区间是。
4. 32x x d dx=⎰_________。
5. 2222x x dx x-+=+⎰。
二、 单项选择题 (每小题3分,共15分)1. 当0x >时，曲线1sin y x x= （ ）。
（A ）有且仅有铅直渐近线. （B ）有且仅有水平渐近线.（C ）既有水平渐近线，又有铅直渐近线. （D ）既无水平渐近线，又无铅直渐近线. 2. 当0x →时，sin x x -是2x 的（ ）。
（A ） 高阶无穷小. （B ） 低阶无穷小.（C ） 等价无穷小. （D ） 同阶但非等价无穷小. 3. 曲线2sin y x x =+在点(,1)22ππ+处的切线方程为（ ）(A) 1y x =-. (B) 2y x π=+.(C) 1y x =+. (D) 12y x π=++.4. 曲线2x y e-=的上凸区间是（ ）。
(A) (-.(B) (,-∞-.(C) 1)+∞. (D) 没有凸区间.5.dx =⎰（ ）。
(A) C +. (B)2tan C x +. (C) 2cos C x +.(D) C +. 三、计算题（一）（每小题 8分，共24分） 1. ()3sin 0lim 12xx x →+ 。
2. 1lim (1)x x x e →∞⎡⎤-⎢⎥⎣⎦。
3. 设函数()y y x =是由方程2xy x y =+所确定的隐函数， 求'(0)y 。
四、计算题（二）（每小题 8分，共 16分）1. 设 2ln(1),arctan ,x t y t t ⎧=+⎨=-⎩ 求 22d ydx 。
2. 求不定积分11x xe dx e -+⎰。
五、求下列各题（每小题 8分，共 16分） 1.计算定积分411dx ⎰。
2. 试问a 为何值时，函数1()sin sin 33f x a x x =+在3x π=处取得极值？它是极大值还是极小值？并求此极值。
六、解答题与证明题（第1小题 8分，第2小题 6分，共 14分）1.确定常数a 和b ，使函数2,1,(),1ax b x f x x x +>⎧=⎨≤⎩ 处处可导。
2. 设()f x 在区间[0,1]上可微，且满足条件：f xf x dx 12(1)2()=⎰，试证: 存在(0,1)ξ∈，使得f f ()'()0ξξξ+=。
南昌大学 2013～2014学年第一学期期末考试试卷及答案一、 填空题(每空 3 分，共 15 分)1.函数1()lg(3)f x x =+- 的定义域是[)()6,22,3-⋃2. 设函数y arctan = 则dy=()1e +3. 函数3(1)(1)y x x =-+的单调增加区间是1,2⎡⎫+∞⎪⎢⎣⎭4. 32x x ddx=⎰25.2222x x dx x-+=+⎰ln3二、 单项选择题 (每小题3分,共15分)1. 当0x >时，曲线1sin y x x= （ B ）。
（A ）有且仅有铅直渐近线. （B ）有且仅有水平渐近线.（C ）既有水平渐近线，又有铅直渐近线. （D ）既无水平渐近线，又无铅直渐近线. 2. 当0x →时，sin x x -是2x 的（ A ）。
（A ） 高阶无穷小. （B ） 低阶无穷小. （C ） 等价无穷小. （D ） 同阶但非等价无穷小. 3. 曲线2sin y x x =+在点(,1)22ππ+处的切线方程为（ C ）(A) 1y x =-. (B) 2y x π=+.(C) 1y x =+. (D) 12y x π=++.4. 曲线2x y e-=的上凸区间是（ A ）。
(A) (.(B) (,-∞-.(C) )+∞. (D) 没有凸区间.5.tan x dx =⎰（ D ）。
(A) C +. (B)2tan C x +. (C) 2cos C x +.(D) C +. 三、计算题（一）（每小题 8分，共24分）1. ()3sin 0lim 12xx x →+ 。
解: 原式()162sin 0lim 12x x xx x ⋅⋅→=+6e =2. 1lim (1)x x x e →∞⎡⎤-⎢⎥⎣⎦。
解: 原式112211l i m l i m 11xxx x e e x x x→∞→∞--==- 1lim 1x x e →∞==3. 设函数()y y x =是由方程2xy x y =+所确定的隐函数， 求'(0)y 。
解: 方程两边对x 求导，有()()2ln2'1'xy y xy y +=+由原方程知 0x =时，1y =，代入上式，得'(0)ln21y =-四、计算题（二）（每小题 8分，共 16分）1. 设 2ln(1),arctan ,x t y t t ⎧=+⎨=-⎩ 求 22d y dx 。
解: 2222121,111dy t dx tdt dt t tt=-==+++. 2dydy t dt dx dx dt∴==.()12dy d dx dt =. 2222112241dy d dy dx d d y tdx dt dx t dx t dxdt t ⎛⎫⎪⎛⎫⎝⎭⎪+⎝⎭∴====+. 2. 求不定积分11x xe dx e -+⎰。
解: 原式12(1)11x x xx x xxe e e e e dx dx e e -+--+==++⎰⎰21xx e dx dx e =-+⎰⎰2ln 1.x e x C =+-+五、求下列各题（每小题 8分，共 16分） 1.计算定积分411dx ⎰。
解:t =，则 2,2x t dx tdt ==，于是原式=2121t dt t+⎰ 221111122111tdt dt t t +-⎛⎫==- ⎪++⎝⎭⎰⎰ []2122ln(1)21ln 3t t ⎛⎫=-+=+ ⎪⎝⎭2. 试问a 为何值时，函数1()sin sin 33f x a x x =+在3x π=处取得极值？它是极大值还是极小值？并求此极值。
解: ()3'()cos cos303x f a x x ππ==+=，得 2a =又3''()(2sin 3sin3)03x f x x ππ==--=<3x π∴=时，()f x取极大值，()3f π=六、解答题与证明题（第1小题 8分，第2小题 6分，共 14分）1.确定常数a 和b ，使函数2,1,(),1ax b x f x x x +>⎧=⎨≤⎩ 处处可导。
解: 当1x ≠时，()f x 显然可导。
当1x =时，因()f x 在1x =处连续，由(10)(10)(1)f f f +=-=，得 1a b += 由2101'(10)lim 21x x f x →---==-，10101'(10)lim lim 11x x ax b ax af a x x →+→++--+===--得 2a =故当2a =，1b =-时，()f x 处处可导。
2. 设()f x 在区间[0,1]上可微，且满足条件：f xf x dx 12(1)2()=⎰，试证: 存在(0,1)ξ∈，使得f f ()'()0ξξξ+=。
证明：设()()F x xf x =，由积分中值定理知，1[0,]2η∃∈，使1/21/21()()()2xf x dx F x dx F η==⎰⎰由已知条件，有1/21(1)2()2()()2f xf x dx F F ηη==⋅=⎰又由于(1)(1)()F f F η==，且()F x 在[,1]η上连续，在(,1)η上可导，故由罗尔定理知：(,1)(0,1)ξη∃∈∈，使'()0F ξ=， 即 ()'()0f f ξξξ+=。