华东理工作业

华东理工大学2020年秋季《大学英语4本》作业1一.单选题1.The hall was almost empty. There were _____ people in it.A、littleB、a littleC、fewD、a few正确答案：C2.When _____ near the horizon, the Moon appears strikingly larger.A、seeingB、sawC、having been seenD、seen正确答案：D3.Bill doesn’t _____ what people say about him.A、concernB、matterC、careD、disturb正确答案：C4._____ the advice of his friends, he would not have suffered such a heavy loss in his business.A、If he tookB、If he should takeC、Were he to takeD、Had he taken正确答案：D5.I don’t want you to make any trouble, _____, I urge you to solve the problem.A、thusB、consequentlyC、on the contraryD、just as正确答案：C6.The heavy rain stopped us _____ at the station on time.A、to arriveB、arriveC、arrivedD、from arriving正确答案：D7.Everything _____ if Albert hadn’t called the fire brigade.A、will be destroyedB、will have been destroyedC、would be destroyedD、would have been destroyed正确答案：D8.I don’t know why he _____ in the middle of a sentence.A、broke awayB、broke outC、broke throughD、broke off正确答案：D9.Unfortunately the poor girl can’t do anything but _____ all her belongings at a low price.A、sellB、to sellC、sellingD、sold正确答案：A10.The president claimed the terrorists should be held responsible _____ the explosions that happened last month in London.A、forB、onC、atD、about正确答案：A11.Do you know who are _____ the survey?A、discussingB、takingC、givingD、conducting正确答案：D12.He _____ himself quickly to the new situation of his work.A、changedB、alteredC、adjustedD、varied正确答案：C13.I’d rather stay at home than _____ a walk.A、takingB、to takeC、takeD、to be taking正确答案：C14.We cannot judge a person simply on the _____ of this education.A、conditionB、basisC、principleD、theory正确答案：B15.It is assumed that students at an intermediate level will have a good _____ of the basic structures and vocabulary of English.A、commandB、commandingC、to commandD、commanded正确答案：A16.Our Lab was being _____ when we visited the university.A、rebuiltB、rebuildC、rebuildingD、to rebuild正确答案：A17.I prefer classic music _____ pop music.A、thanB、onC、withD、to正确答案：D18.I’m old enough to wash _____ clothes by myself. You can just wash _____.A、my,yourB、mine,yoursC、my,yoursD、your,my正确答案：C19.A lecture hall is _____ where students attend lectures.A、thereB、whichC、oneD、that正确答案：C20.He spoke so quickly that I didn’t _____ what he said.A、make forB、make sureC、make overD、make out正确答案：D。

一、判断(共计50分,每题2.5分)1、K[AlSi3O8]是一种岛状结构的硅酸盐。

A.正确B.错误参考答案：【B】2、选择灰铸铁而不是低碳钢用于制造铸件是基于其工艺性能的考量。

A.正确B.错误参考答案：【A】3、马氏体相变是正扩散相变。

A.正确B.错误参考答案：【B】4、如果某金属是面心立方晶胞的结构，那么一个晶胞中含有两个原子。

A.正确B.错误参考答案：【B】5、一般来说，对于固相反应体系，扩散速率远高于化学反应速率。

A.正确B.错误参考答案：【B】6、烧结初期的传质过程主要为颗粒间的粘附作用。

A.正确B.错误参考答案：【A】7、对于许多物理或化学步骤综合而成的在固相反应中，反应速度由反应速度最慢的步骤控制。

A.正确B.错误参考答案：【A】8、硅酸盐熔体中，形成玻璃的倾向大小和熔体中负离子团的聚合程度有关，聚合程度越低，越不容易形成玻璃，聚合程度越高，越容易形成玻璃。

A.正确B.错误参考答案：【A】9、透明陶瓷是烧结的密实体。

A.正确B.错误参考答案：【A】10、如果某金属是简单立方晶胞的结构，那么一个晶胞中含有8个原子。

A.正确B.错误参考答案：【B】11、一般来说，在烧结过程中施加压力可以加速烧结过程的进行。

A.正确B.错误参考答案：【A】12、固相反应的开始温度，远低于反应物的熔点或者系统的低共融温度。

A.正确B.错误参考答案：【A】13、杨德方程适用于固相反应动力学求解。

A.正确B.错误参考答案：【B】14、固相反应过程主要包括界面上的化学反应和产物内部物质传递两个步骤。

A.正确B.错误参考答案：【A】15、第一代材料都取自于自然界已有的资源，没有化学合成。

A.正确B.错误参考答案：【A】16、成核-生长相变是负扩散相变。

A.正确B.错误参考答案：【B】17、对于成核生长相变，温度越低，成核速率越快。

A.正确B.错误参考答案：【B】18、若相变过程放热，相变过程要自发进行则系统需要“过冷”。

第1题、It is not that I do not like plays. The reason why I did not go to the theater last night was that I could not ___ the time.A、offerB、leaveC、affordD、manage标准答案:C第2题、To speak English well, ___.A、much practice is neededB、one needs much practiceC、much practice is needed by oneD、one is needed much practice标准答案:B第3题、The material produced in China ___ easily.A、is washedB、washesC、washingD、are washing标准答案:B第4题、I am pleased to take ___ to exchange views with you.A、this opportunityB、a chanceC、this timeD、a period标准答案:A第5题、It is required ___ me that I give evidence.A、ofB、fromC、forD、with标准答案:A第6题、Canned foods are ___ with housewives because it takes so little time to cook them.A、popularB、welcomeC、desirableD、usual标准答案:A第7题、As a senior, please give me ___ advice you can give on this issue.A、thatB、whatC、whichD、whatever标准答案:D第8题、The committee proposed that more emphasis should be laid ___ developing practical skills in students.A、ontoB、toC、onD、over标准答案:C第9题、Most of the residents near the airport have all moved as they can not stand ___ in such a moisy place.A、to liveB、liveC、livingD、be living标准答案:C第10题、The new order will mean ___ overtime.A、to workB、workingC、workD、to be working标准答案:B第11题、Some pop singers have much influence ___ the young people today.A、toB、forC、ontoD、on标准答案:D第12题、The mistake was ___ by the carelessness of the assistant.A、dueB、causedD、owe标准答案:B第13题、The hall was almost empty. There were ___ people in it.A、littleB、a littleC、fewD、a few标准答案:C第14题、There ___ not much milk in the refrigerator, ___A、is…isn't thereB、are…are thereC、is…is thereD、are…aren't there标准答案:C第15题、A new driver can not be ___ careful in driving a car.A、veryB、quiteC、ratherD、too标准答案:D第16题、Of the six people in the plane that crashed, only one ___.A、enduredB、survivedD、retained标准答案:B第17题、The passengers desire that the airline ___ them immediately of any change in flight time.A、informB、informsC、informedD、has informed标准答案:A第18题、They carry ___ with their work in spite of the extremely difficult conditions.A、outB、overC、onD、back标准答案:C第19题、You should make ___ your house or flat is secure.A、sureB、certainC、understandingD、knowledge标准答案:A第20题、He ___ a knowledge of the language by careful study.B、earnedC、gainedD、acquired标准答案:D第21题、He is a kind-hearted and ___ gentleman.A、respectiveB、respectableC、respectedD、respectful标准答案:B第22题、She ___ a post at Yale University.A、took onB、took toC、took upD、took in标准答案:C第23题、The opening of a new school is always a great ___.A、chanceB、occasionC、incidentD、opportunity标准答案:B第24题、Hangzhou is an ideal place to settle down after retirement ___ it hasbeautiful scenic spots nearby and a far slower pace of life.A、provided thatB、now thatC、so thatD、in that标准答案:D第25题、The boss ___ the young man that he would receive a raise.A、securedB、insuredC、ensuredD、assured标准答案:D第26题、Wealthy as he is, he is not ___ with his money, unwilling to help others in troubles.A、carefulB、generousC、satisfiedD、busy标准答案:B第27题、The president claimed the terrorists should be held responsible ___ the explosions that happened last month in London.A、onB、atC、forD、about标准答案:C第28题、She is very careful. She ___ very few mistakes in her work.A、doesB、takesC、makesD、gets标准答案:C第29题、It is difficult to __ a conversation with all this noise around us.A、carry onB、account forC、bring upD、get through标准答案:A第30题、By the time Martin Luther King delivered his famous speech, the blacks ___ with the white in the same classroom.A、had never before studiedB、never before studiedC、couldn't have studiedD、have never before studied标准答案:A第31题、We wrote an article last month, and it turns out to be a success, so we begin to work on ___ one this month.A、anotherB、moreD、other标准答案:A第32题、No agreement was reached in the discussion, as __ side would give way to the other.A、noneB、bothC、eitherD、neither标准答案:D第33题、What will happen to you, if you ___ in your school workA、fall downB、fall apartC、fall offD、fall behind标准答案:A第34题、He suffered terrible injuries, but his courage pulled him ___.A、outB、upC、throughD、over标准答案:C第35题、In this factory each worker must receive a ___ training course.A、two-monthC、two-monthsD、two-months'标准答案:A第36题、They handed in their paper ___.A、in lineB、by turnC、at turnD、in turn标准答案:D第37题、___ her interest in children, I am sure teaching is the right career for her.A、GivenB、GivingC、To giveD、To be given标准答案:A第38题、I had the good ___ to be chosen for a trip abroad.A、propertyB、estateC、wealthD、fortune标准答案:D第39题、No one can possibly racall any detail about the meeting. It is at leastfive years since it ___.A、had taken placeB、was taken placeC、took placeD、was taking place标准答案:C第40题、I prefer live in the countryside. Country life has a lot of ___ over city life.A、characterB、qualitiesC、advantagesD、ways标准答案:C第41题、You ___ all the way from the station to my place! You can take a taxi.A、needn't have walkedB、shouldn't have walkedC、must not have walkedD、cannot have walked标准答案:A第42题、I believe you have ___ some important points in the report.A、left aloneB、left behindC、left offD、left out标准答案:D第43题、I prefer classic music ___ pop music.A、thanB、onC、withD、to标准答案:D第44题、I ___ you that I had no intention of offending you.A、convinceB、persuadeC、guaranteeD、assure标准答案:D第45题、She has always ___ to her father, although he did not graduate from a famous university.A、appreciatedB、admiredC、respectedD、looked up标准答案:D第46题、The parents spoil their child by buying anything he wants, ___.A、however much it costsB、however does it costs muchC、how much does it costD、no matter how it costs标准答案:A第47题、The act of speaking will also help to improve listening comprehension ___.A、to some wayB、in the wayC、to some extentD、in the extent标准答案:C第48题、Some of the citizens have been ___ medals for bravery.A、givenB、offeredC、awardedD、paid标准答案:C第49题、I want to make it clear that I am utterly opposed ___ any form of terrorism.A、againstB、toC、forD、with标准答案:B第50题、We wanted to go on a picnic. But the wind ___ strong, we had no choice but to stay indoors.A、beingB、had beenC、wasD、was being标准答案:A第51题、The president made his last public ___ before his term of office ended.A、engagementB、appearanceC、meetingD、gathering标准答案:B第52题、I did not buy the same book ___.A、what he boughtB、that he boughtC、as he boughtD、which he bought标准答案:C第53题、She was ___ the top prize in the competition.A、awardedB、rewardedC、receivedD、accepted标准答案:A第54题、The teacher ___, the children in the classroom burst into talking instantly.A、having leftB、leftC、leaving标准答案:A第55题、Perhaps some day it will be pleasant to ___ these things.A、look down onB、look forward toC、look back onD、look on标准答案:C第56题、Chinese must develop science and technology at a high speed ___ catch up with the latest development in other countries.A、so toB、so as toC、as toD、so标准答案:B第57题、The cost of computer used to be ___ for me, but now I can afford it.A、so muchB、too muchC、very muchD、much too标准答案:B第58题、He ___ a six-year-old child as he was driving back from a party.A、ran acrossB、ran intoD、ran through标准答案:C第59题、The old lady who suffers from lung cancer ___ at the moment.A、is being operated onB、is operated onC、operates onD、to be operated on标准答案:A第60题、Did you have a neighbor who was always ___ your businessA、doingB、makingitC、getting aboveD、poking his nose into标准答案:D第61题、Tony could be a very successful student, but he ___ no importance to study.A、attachesB、attachedC、was attachingD、had attached标准答案:A第62题、She used to be an ordinary girl, what on earth has made her ___ she is todayA、thatB、whatD、as标准答案:B第63题、I want to update my English ability, but I have no idea what kind of material ___.A、to listen toB、listening toC、for listeningD、to listen标准答案:A第64题、She can speak French and German, to ___ nothing of English.A、sayB、speakC、talkD、tell标准答案:A第65题、Mary offered to keep an eye ___ the baby while I was away.A、atB、forC、inD、on标准答案:D第66题、I saw she was in a difficulty with all those parcels, so I offered my ___.A、servicesC、useD、chance标准答案:A第67题、In this remote island, the people who had survived the ship accident made use of ___ for a living.A、every means availableB、every available meansC、every mean availableD、every available mean标准答案:A第68题、He is uncertain about ___ to see her tonight.A、whichB、whetherC、thatD、what标准答案:B第69题、It ___ that I met one of my old classmates on my way home yesterday.A、took placeB、occurredC、broke outD、happened标准答案:D第70题、My parents are not interested in modern music. They are ___ the times.B、behindC、afterD、low标准答案:B第71题、His attitude toward us seems ___.A、nicelyB、warmlyC、kindlyD、friendly标准答案:D第72题、Dr. Hoffman proposed that we ___ the meeting until next week.A、put offB、to put offC、putting offD、need put off标准答案:A第73题、Which events are you ___ at the school sportsA、going back onB、going in forC、getting down onD、getting along with标准答案:B第74题、We have kept ___ our friendship by writing to each other, so we are trueA、upB、backC、offD、down标准答案:A第75题、Having heard so much about Mr. Smith, they were ___ to meet and have a chat with him.A、eagerB、desperateC、urgentD、earnest标准答案:A第76题、The man ___ the gate when he realized that we had spotted him.A、made offB、made outC、made forD、made up标准答案:C第77题、I estimate that my vocabulary might be three times ___ it was two years ago.A、thatB、whatC、whichD、than第78题、According to many learners, Chinese is not easy ___.A、to be learnedB、learningC、to learnD、having learned标准答案:C第79题、The population of the world is growing at a dangerous ___.A、progressB、rateC、increaseD、measure标准答案:B第80题、The teacher spoke so fast that it was hard for the students to ___ what he was saying.A、take inB、take outC、take upD、take over标准答案:A第81题、I do not know him very well so I cannot tell exactly what it is ___ prevents him from making progress.A、of whichB、whoD、that标准答案:D第82题、___ I myself sees a ghost, I will not believe any second-hand supersitious description about it.A、UnlessB、WhenC、AsD、While标准答案:A第83题、The star was ___ the scientist who found it.A、looked afterB、taken afterC、named afterD、come after标准答案:C第84题、He gave to his friends what he ___ to his family.A、declinedB、refusedC、rejectedD、denied标准答案:D第85题、You should be more ___ to the elderly people.A、respectableB、respectfulC、remarkableD、respective标准答案:B第86题、___ from space, our earth, with water covering 70 percent of its surface, looks like a blue planet.A、SeenB、SeeingC、Having seenD、To see标准答案:A第87题、I had planed to go to a secondary school after junior high school, but my parents suggested that I ___ senior high school.A、to goB、goC、goingD、went标准答案:B第88题、Every time I go to the West Lake, I find myself ___ to the scenery around it.A、drawsB、drawingC、drawnD、drew标准答案:C第89题、Nobody but a young woman ___ the airplane crash.A、enduredB、rejectedC、survivedD、lived标准答案:C第90题、If you have made a decision, please stick ___ what you want.A、toB、upC、ofD、for标准答案:A第91题、I did not apply for a credit card last year, but I ___.A、had appliedB、should have appliedC、should applyD、would apply标准答案:B第92题、We failed in our ___ to climb the mountain.A、trialB、contemptC、desireD、attempt标准答案:D第93题、He has never been able to ___ a job for long.A、hold downB、hold forthC、hold withD、hold off标准答案:A第94题、Mr. Smith ___ a most important part in the development of our city.A、tookB、hadC、playedD、made标准答案:C第95题、How the fire in the dance hall started ___ a mystery.A、to remainB、remainsC、remainD、is remaining标准答案:B第96题、They promised him he would soon be rich ___ his wildest dreams.A、overB、byC、beyondD、for标准答案:C第97题、I want to know what she ___ before I will vote for her.A、stand forB、care forC、call forD、go for标准答案:A第98题、They want all the groups to be treated on a ___ of equality.A、bassB、baseC、basisD、basement标准答案:C第99题、Three people, ___ a child, were injured in the accident.A、includedB、includeC、includingD、includes标准答案:C。

2021年秋季安全技术网上作业一、单选题1.(5分)热量传递的基本方式不包括（）A. 热辐射B.热循环C. 热对流D. 热传导2.(5分)不属于有毒化学品发生燃烧爆炸事故时对人员和环境的危害是（）。

A. 腐蚀性的破坏作用B. 高温的破坏作用C. 爆炸的破坏作用D. 造成中毒和环境污染3.(5分)C类火灾指的是（）火灾。

A. 固体物质B. 液体物质C. 气体物质4.(5分)动火前，动火证应交（）检查，确认安全措施已落实无误后，方可按规定时间、地点、内容进行动火作业。

A. 质量监督部门B. 安全员C. 现场负责人D. 地方政府消防安全管理部门5.(5分)易燃液体在运输、泵送、灌装时要有良好的（）装置，防止静电积聚。

A. 防火B. 接地C. 监测6.(5分)高温设备不能急骤降温，一般要求设备内介质温度要（）A. 低于60℃B. 高于60℃C. 低于80℃D. 高于80℃7.(5分)通常的爆炸极限是在常温、常压的标准条件下测定出来的，它随（）的变化而变化。

A. 温度、容积B. 压力、容积C. 压力、温度二、多选题1.(5分)最佳设备布置要达到（）要求。

A. 满足工艺流程路径B. 设备排列紧凑C. 经济合理D. 整齐美观E. 节约投资2.(5分)危险化学品中毒、污染事故的预防控制措施有（）A. 密闭B. 隔离C. 通风D. 替代E. 个体防护3.(5分)在化学工业中，对于过程单元本身的安全评价，比较重要的因素有（）A. 操作温度B. 操作压力C. 单元中物料的类型D. 单元中物料的量E. 单元的固定投资额4.(5分)氧化反应的主要危险性有（）A. 反应中的有些氧化剂本身是强氧化剂，具有很大的危险性B. 反应的产品也具有火灾、爆炸危险性C. 反应中被氧化的物质大部分是易燃、易爆物质D. 反应是在氢气存在的条件下，并在高温、高压下进行，极易发生爆炸E. 反应需要加热，同时绝大多数反应又是放热反应，因此，反应热如不及时移去，将会造成反应失控，甚至发生爆炸5.(5分)（）灭火器适于扑灭电气火灾。

华东理工大学复变函数与积分变换作业（第1册）班级____________学号_____________姓名_____________任课教师_____________第一次作业教学内容：复数及其运算 平面点集的一般概念1．填空题：（1）35arctan 2,234,2523,25,23-+-πk i (2)3arctan 2,10,31,3,1-+-πk i（3）)31(21i +- (4) 13,1=-=y x 。

2．将下列复数化成三角表示式和指数表示式。

(1)31i +; 解：32)3sin 3(cos 2)2321(231πππi e i i i =+=+=+ (2))0(sin cos 1πϕϕϕ≤≤+-i 解：)22(2sin 2)]22sin()22[cos(2sin 2sin cos 1ϕπϕϕπϕπϕϕϕ-=-+-=+-i e i i(3)32)3sin 3(cos )5sin 5(cos φφφφi i -+. 解：φφφφφφφφφ199********)/()()3sin 3(cos )5sin 5(cos i i i i i e ee e e i i ===-+-- φε19sin 19cos i +3．求复数11+-z z 的实部与虚部 解：2|1|)1)(1()1)(1()1)(1(11++-=+++-=+-=z z z z z z z z z w 222|1|Im 2|1|1|1|)1(+++-=+--+=z z i z z z z z z z z 所以，2|1|1Re +-=z z z w ，2|1|Im 2Im +=z z w 4. 求方程083=+z 的所有的根. 解：.2,1,0,2)8()21(331==-=+k e z k i π即原方程有如下三个解：31,2,31i i --+5. 若 321z z z ==且0321=++z z z ，证明：以321,,z z z 为顶点的三角形是正三角形. 证明：记a z =||1，则232232223221)(2z z z z z z z --+=+= 得22323||a z z =-221|)||(|z z -=，同样，22212123||a z z z z =-=- 所以.||||212321z z z z z z -=-=-6. 设2,1z z 是两个复数，试证明. 212z z ++221z z -22122()z z =+. 并说明此等式的几何意义.证明： 左式=(21z z +)(21z z +)+(21z z +)(21z z -)=(21z z +)(21z z +)+(21z z +)(21z z -) =2121221121212211z z z z z z z z z z z z z z z z ⋅-⋅-⋅+⋅+⋅+⋅+⋅+⋅ =2(2221z z z z ⋅+⋅)=2(2221z z +)7．求下列各式的值: (1)5)3(i -; 解：5)3(i -=6556532)2()223(2ππi i e e i --==⎥⎦⎤⎢⎣⎡- =i i 16316)65sin()65cos(32--=⎥⎦⎤⎢⎣⎡-+-ππ (2)31)1(i -；解: 31)1(i -.2,1,0,2)2()221(23)24(631431===⎥⎦⎤⎢⎣⎡-=+--k e e i k i i πππ 可知31)1(i -的3个值分别是)12sin 12(cos 22626πππi e i -=-；)127sin 127(cos 226276πππi e i += )45sin 45(cos226456πππi e i += （3）求61-解：61-=.5,4,3,2,1,0,)(6/)21(612-=++k e e k i k i πππ可知61-的6个值分别是 223,1,2236526i ei e i e i i i +-==+=πππ223,,2234112367i e i e i ei i i -=-=--=πππ (4) ()()()()1001001001005050511+i +1-i =cos +isin +cos -isin 4444 =2cos 25+isin 25+2cos 25-isin 25 =-2ππππππππ⎤⎤⎫⎫⎪⎪⎥⎥⎭⎭⎦⎦8．化简2)1()1(--+n ni i 解：原式1222211)1(+-=-=⎪⎭⎫ ⎝⎛-+-=n i n n i ie i i i π第二次作业教学内容： 平面点集的一般概念 复变函数1. 填空题(1)连接点i +1与i 41--的直线断的参数方程为10)52(1≤≤--++=t t i i z(2)以原点为中心，焦点在实轴上，长轴为a ，短轴为b 的椭圆的参数方程为π20sin cos ≤≤+=t t ib t a z2．指出下列各题中点z 的轨迹，并作图. (1)12≥-i z ;中心在i 2-半径为1的圆周及其外部。

华东理工高等数学作业本第1次作业答案第3章（之3）第15次作业教学内容: §3.3.1 00型3.3.2 ∞∞型1. 填空题*（1）若0≠p ，则px px xx x cos sin 1cos sin 1lim0-+-+→________=.解：p 1.**（2）_______)e1ln()e 1ln(lim11=+--+-∞→x x x .解：2e -。

2. 选择题。

**（1）若)()(limx g x f x x →是00待定型，则“Ax g x f x x =''→)()(lim 0”是“Ax g x f x x =→)()(lim 0”的（ B ）（A ）充要条件； (B)充分条件，非必要条件；（C ）必要条件，非充分条件； (D) 既非充分条件，也非必要条件.**（2）若)()(limx g x f x x →是∞∞的未定型，且Ax g x f x x =''→)()(lim 0，则=→)(ln )(ln lim 0x g x f x x（ B ）（A ）A ln ；（B ）1； (C)2A ； (D)21A.***3 求极限 xx x xxx arctan 3 3e2elim220---+-→.解：原式= =+----→2201116e2e2limxxxxx 2203e elim2xxx xx ---→xxxx 23e e2lim220-+=-→31ee4lim20=-=--→xxx .4 求下列极限:**（1）+→0lim x )0()sin ln()sin ln(>>a b bx ax ； **（2）∞→x lim)43ln()35ln(236+-++x x x x .解：（1）原式bxa x cos cot lim+→=ax b bxa x tan tan lim+→=1=.（2）)431ln(ln )751ln(ln lim 22636x x x x x x x +-++++=∞→原式=++++-+→∞limln()ln ln()ln x x xxx x x 3157113436222=3.****5. xex x x -+→1)1(lim.解： ])1[(lim )00()1(lim 10'+=-+→→xx x x x x e x 210)1()1)](1ln()1([lim x x x x x x x x ++++-=→2]21)1ln(1lim[])1ln()1(lim[02e xx e xx x x e x x -=-+-=++-=→→.***6. 若已知()x f '在0=x 连续，且有()00=f ，2)0(='f ，求极限()()[]2limxx f f x f x ?→.解：xx f f xx f xx f f xx f xx f f x f x x x x )]([lim)(lim)]([)(lim)]([)(lim2→→→→?=?=?82)]0('[)]0('[)0(')('1)](['lim1)('lim3320===?=??=→→f f f x f x f f x f x x .***7. 设()x f 具有2阶连续导数，且()00=f ，试证()x g 有1阶连续导数，其中()()()??=≠=.0,0,0,'x f x xx f x g证明：依题意，当0≠x 时，2)()(')('xx f x x f x g -?=均连续.故只需证明 )0(')('lim 0g x g x =→ 即可.由导数定义，有)0("212)0(')('lim)0(')(lim)0(')(lim0)0()(lim)0('02f xf x f xxf x f xf xx f x g x g g x x x x = -=-=-=--=→→→→又)0(')0(''212)(')(')(''lim)()('lim)('lim 020g f xx f x f x x f xx f x x f x g x x x == -+=-=→→→.故命题得证.。