考研英语复习

2011研英全程五轮四阶全计划

一阶基础复习规划(3-6月份)

主要目标：掌握大纲要求的词汇及短语，全面复习语法，争取语法无盲点。

大家都知道英语学习中如果词汇不掌握，对考试来说是非常不利的，很多同学说自己有技巧，但是如果连题目都看不懂的话，有技巧去哪里施展呀，尤其是英语考试，通篇的英语词汇，这时，谁知道的词汇谁就占了优势；还有同学会说，大纲没有明确提出语法，而且考试也不专门考查语法题，但是为什么有些同学单词都认识，但是句子，文章还是读不懂，当然就是语法没有掌握，而且翻译题，主要考查的就是词汇，语法和语言组织能力，可见词汇和语法是英语复习中的基础，所以我们放在第一阶段。

大家要注意，只有做好这个阶段，顺利完成这个阶段的任务，才会更顺利的进行下面的复习。

复习中注意几个问题：

(1)要根据自己的具体情况量身制定复习计划

做任何事情都要有计划，考试复习更是如此，英语的基础阶段词汇的不需要大量的做题，只需要大量的阅读，大家应该在复习内容量化，譬如说每天看一单元单词(30～50页为一单元)，语法的学习比较枯燥，所以在要练习题中巩固及复习自己的语法盲点。

(2)关于词汇复习的建议

无论选择哪本词汇书，当然大纲是最好的，可以把这本词汇书平均分成7个单元，这样每天早上早起15分钟，晚上晚睡15分钟，利用这个挤出来的时间看单词，大家注意一下，我这里用的是看，所以不要背，第一遍的任务就是先混个眼熟，把不认识的单词标出来(如果不认识的多于认识的，那就把认识的标出来)，词义只看第一二个核心的意思即可。这样一个月就可以看四遍词汇，三个月下来是十二遍，不想记住也难了。

当然以上看词汇是没有用我们真正的复习时间的，我们做计划时也不应该列入其中，这样就省了很多时间。真正的复习时间是用来背核心词汇的，大家可以把历年考题中最重要的核心词汇拿来巩固。

(3)强调积极主动地亲自参与，并整理出笔记

注意一定要在学习过程中写出自己的感受，可以在书上以题注的形式或者就是做笔记，把自己做错或者不扎实的题记下来，这一点很重要，并且要贯彻前三轮的复习，如果最后一轮复习我们有了自己整理的笔记，就会很轻松。

二阶强化复习规划(7-10月份)

主要目标：阅读及翻译达标，提高阅读速度，巩固词汇的运用能力。

众所周知，考研英语试卷中，阅读理解分值比重占了半壁江山还多，“得阅读者得天下”，此言不虚。但阅读能力的培养是个系统工程，要想在一定时间内得以快速提升，我们必须从四个方面入手学习：词汇的认知、难句的分析、篇章的把握和解题的套路。只有在“词、句、篇、题”这四个层面做到“合四为一”的精读，才能实现“阅读”、“理解”和“解题”的完美结合，切实提升阅读理解的“内功”和“招法”。

复习建议：

英语学习是个循序渐进的过程，阅读能力的提升也非一日千里，考生可根据自身情况制定本阶段符合自己的“阅读学习计划”：

“两遍”阅读法：

第一遍“略读”：严格按照考试要求，在规定时间内通读文章、完成题目。以“大体了解文章中心思想和重点信息”为主旨，以解答题目作为目标。切不可拘泥于个别的词、句等语言细节，应注重培养实战感觉，稳定阅读速度，提升对文章整体的逻辑理解力。

第二遍“精读”：所谓“精读”，即要从词、句、篇、题四个层面对文章进行细读和研读，充分汲取每一篇文章的营养，全方位夯实自己的语言实力。具体而言，生词要理解记忆；难句要分析翻译；篇章结构也要梳理，提炼出每段的大意和篇章的主旨，进而理出文章的行文脉络；题目不要机械地对答案，要见木见林，做对的题要提炼思路，归纳方法，做错的题目要错误分析，汲取教训。

复习的重要性：

复习是被很多考生做阅读时所遗忘的一个环节。殊不知，每读完一篇文章，里面的“得”与“失”都是考生成长过程中难能可贵的养分。所以，我们必须及时地、反复地复习，不断来摄取这

些养料，知道考试前的最后一周。切记“题海”战术，要相信四千道题做一遍的效果绝对比不上一千道题做四遍的效果；与其博览群书，不如精读一本。

三阶模考冲刺复习规划(11-12月中旬)

主要目标：利用套题对前面的复习做一个总体的检验，练习答题规范，保持卷面整洁，增加信心，练习掌握考试时间的分配，增强临场应变的能力，要对自己前两个阶段复习中出现含糊不清，掌握不牢的地方重点加强。

经过上面两轮的准备，考生的能力和思维储备已经足够应付考研试题了。在这个阶段里，考生应该开始进行模拟试题或者真题的实战演练，在这个过程中，注意答卷时间的分配，重视考场心态的调整。无论自己的模拟考试成绩如何，都要保持良好的心态：分数考高了，不要洋洋自得，毕竟真实的考场上压力和环境都和平时不太一样；分数考低了，也别灰心丧气，认真总结经验教训，况且一般来说模拟题都要难于真题。

注意问题：

这个阶段的复习中我们需要特别注意的一点就是对真题答题规范的研究。因为考试题量大，时间紧，很多同学都会有时间不够的感觉，再次强调研究真题主要是针对整张试卷和答题规范的把握。按照规范，需要写的不要落掉，不需要写的，我们争取不写，这样的话，一方面我们可以节省时间，另一方面可以规范我们的思路，只有平时养成良好的习惯，考试的时候才能做到心中有数，不至于惊慌失措。由于真题有限，所以我们应该重复这个训练过程，直到我们对自己满意了为止。

第二个问题就是要做好总结与归纳，自己不扎实的题以及出过错误的题，都要全部记录下来。在这个阶段不应该还有盲点了，自己做整体的梳理，总结和归纳。

复习的重要性：

复习是被很多考生做阅读时所遗忘的一个环节。殊不知，每读完一篇文章，里面的“得”与“失”都是考生成长过程中难能可贵的养分。所以，我们必须及时地、反复地复习，不断来摄取这些养料，知道考试前的最后一周。切记“题海”战术，要相信四千道题做一遍的效果绝对比不上一千道题做四遍的效果；与其博览群书，不如精读一本。

四阶点睛复习规划(12月中旬-考试)

主要目标：强化记忆，背诵模板，调整心态，保持状态，积极应考。

由于长时间较为艰苦的复习，到了最后时刻的复习阶段，考生心理和生理都难免会感到疲惫，而此时恰恰是复习最关键的时候。这个时候我们原来书页的空白处还有笔记本上总结的东西就有大用了。因为是自己的总结，所以看这些东西，对我们自己而言更有针对性，让我们可以很快地恢复状态，加深记忆。在此基础上，最好按照考试时间去做一些强度不太大的模拟题或者已经作过的真题，让自己保持手感。在一个良好的复习心态下积极备考，是最后的复习阶段中至关重要的。

时间是磨练一个人意志最合适的武器。再回首是否还记得当初毅然选择考研来改变命运、创造辉煌未来的初衷？然而, 经过基础及系统阶段的学习，越是到了冲刺阶段，大多数考生反而会在模拟试题或历年真题的历练中发挥不出原有的水平，且产生了焦虑和紧张的焦灼情绪。这是历年考研考生冲刺阶段所表现出的正常现象，请大家不要发慌，安下心来按部就班的完成学习计划就是度过这个瓶颈期的最好方法。只要全身心的去投入，就一定会有所收获。

生活是一个体验和解决各种困难的过程，而考研的过程亦是不断解决各种困难的过程，不存在困难是不符合客观的，想一下子解决所有的困难或者将困难解决没有了同样是不可能的,

因此无论复习到什么程度, 都应该放下包袱, 我们所要做的就是将自己掌握的全部知识正常

发挥在卷面即可。在备考过程中不要花费精力去否定自己, 要相信只要自己冷静思考，沉着面对, 就会有所回报。

每个人的精力是有限的, 每天的时间也是有限的，因此不可能每件事都做到完美，所以, 最重要的是记得先做最重要的事情，必须要做好的，也就是能左右大局的事情，而其他的也就是不重要的，也不要去花费时间和精力的。切忌不分主次的眉毛胡子一把抓，到最后该做的事一件也没做好。要正视一切能想到的成功的因素, 没有侥幸心理的去诚实面对。这里包括了精神和心理状态,在复习中时刻培养自己的自信心, 不断的鼓励自己, 在漫长孤独的复习中坚持下去, 能坚持到最后, 才能在考试中成功。

大学、研究生阶段论文写作考试复习资料

Chapter 1 Defining the Dissertation You are asked to write a term paper,a library paper,a review,or a book review in order to demonstrate that you have learned the necessary skills of a general academic ability in the subject taught during the semester. How to define the terms like thesis,dissertation,paper(all be translated into Lun wen论文) vs their relationship. Dissertation is used to refer to "a long essay that you do as part of a degree or other qualification"that you are studying for -that is,a BA or an MA. Thesis is used to refer to "a long piece of writing,based on your own ideas and research that you do as part of your university degree,especially a PhD. So if the assay is part of a BA or MA degree,we call it a dissertation,if a part of a PhD degree we call it a thesis.You write an essay for a certain course during your university studies,we it a paper. BA dissertation学士论文,an MA dissertation硕士论文,a PhD thesis博士论文, term paper论文.Here is in line with the British educational tradition. In America,thesis means a BA lun wen or MA lun wen. Dissertation means a PhD lun wen. thesis,dissertation, and paper,their writing process is more or less the same,the major difference between them lies at the level of originality. Difference and relationship between a summary of information (easier to prepare)and an evaluation of information(include a summary) . Academic writing,term paper or research article can aim at summarizing other's studies in the field and presenting the ideas or arguments put forward by other scholars.By contrast,a dissertation or thesis requires more than an acknowledgement of existing studies,it must involve a critical evaluation of research information and this is where the originality of the study lies. When summarize existing studies in the field,you are expected to present to the reader what you have read,how much you have understood,the way you organize all the information. When expected to evaluate previous studies,you must show ability in understanding ,commenting in a scholarly way,consider what factor,how and why factors. A dissertation involves both summarizing and evaluating other's studies in this field,this part of the work is called Literature review. The process of writing a dissertation,steps:we need a kind of yo-yo approach (go backward and forward)proposed by Sorenson ,do not think research process is direct or straightforward. Writing a dissertation is going through a process of doing research.3 steps in process:1.prewriting 2.writing 3.editing and completion. Chapter 2 Basic Writing and Academic Writing Two types of writing(different genre types and reflect different level of difficulties): 1.Basic Writing or practical writing (every day writing and all of us do it) 2.Academic Writing(only required in an academic environment) Purpose of Basic Writing:help students learn to write well for everyday purpose,focus is on general writing skills and strategies.Different types of essays:narration,description,exposition,argumentation. Precis writing:(abstract the main points of an essay ,report,book). It is similar to the writing of summaries(the condensation of information)

自动化考研方向及学校排名

控制理论与控制工程 课程设置矩阵论，泛函分析，线性系统理论，优化理论与最优控制，非线性控制系统理论，智能控制，自适应控制，鲁棒控制，系统辨识与建模，随机过程与随机控制，离散事件系统理论，控制系统的计算机辅助设计与仿真，机器人控制等。 检测技术与自动化装置 课程设置矩阵分析，数学物理方程，误差分析，现代控制理论，近代物理基础，电磁场理论，检测理论，信号处理，传感器与自动检测技术，自动测试与故障诊断技术，仪表智能化技术，仪表可靠性技术，工业计算机网络和集散控制系统，过程模型化与软测量技术等。

系统工程 课程设置数理统计及随机过程，矩阵论，最优化理论与方法，系统工程导论，系统工程方法论，管理信息系统与决策支持系统，信息工程，系统建模与仿真，现代控制理论基础，智能控制，计算机网络理论与技术，复杂系统分析，经济系统分析（宏观和微观）等。 模式识别与智能系统 课程设置随机过程与数理统计，矩阵论，优化理论，近世代数，数理逻辑，数字信号处理，图象处理与分析，模式识别，计算机视觉，人工智能，机器人

学，计算智能，非线性理论（如分形、混沌等），控制理论，系统分析与决策，计算机网络理论等。 导航、制导与控制 课程设置矩阵论，泛函分析，数值分析，线性系统理论，随机过程与滤波，系统辨识，计算机控制系统，最优控制，运动体控制与制导系统，导航系统，火力控制技术，传感技术及应用，信息融合技术，系统建模与仿真，人工智能等。 控制理论与控制工程排名学科代码：081101 1 清华大学A++ 081101控制理论与控制工程 2 山东大学A++ 081101控制理论与控制工程 3 北京科技大学A++ 081101控制理论与控制工程

考研英语作文范文八篇

一、网恋 Directions: Write an essay entitled On-line Love Affair, your essay should meet the requirements below: (1)its side-effect (2)your viewpoints You should write 160~200words neatly on ANSWER SHEET 2. 背诵范文： Although the popular belief is that internet increasingly plays an important role in our daily life, a current survey indicates that it has also brought some youngsters great disadvantages. They can do whatever they like, such matters as playing games, chatting. And some are even falling in love with chatters, which is called on-line love. Fresh notion as on-line love is, it sounds ridiculous when analyzed profoundly. What these young people fail to understand is that both sides have not well acquainted with mutually. Some net friends are reported to have been deceived by those people who are doing some criminal activities per year through the internet. Internet has indubitably provided various information for us, and on-line love is nothing but an artifact of fictitious world offered by internet. On the other hand, it is vital that we should make internet serve us better, and at the same time,as far as on-line love is concerned, being objective and levelheaded analysis is not far from being a sensible attitude. 范文精译： 尽管大家普遍认为网络在我们的日常生活中越来越重要，但当前的调查表明它同时也给一些年轻人带来了弊端。人们可以通过网络做他们喜欢做的一切，诸如打游戏、聊天。有些人甚至与聊天者谈起了恋爱，这就是所谓的网恋。 尽管网恋比较新颖，但仔细分析过后不免有些荒唐。这些年轻人没有意识到他们双方并不彼此了解。据报道，每年都有网友被那些专门通过网络做非法勾当的人欺骗。 毋庸置疑，网络给我们提供了各种各样的信息，而网恋只不过是网络这个虚幻世界的产物。一方面，我们应该使网络更好地为我们服务；同时就网恋而言，客观对待、冷静分析才是明智之举。 二、论美女经济 Directions: Write an essay with the title of On“Beauty Economy”，and your essay should be based on the following outline : (1)describe briefly the phenomenon of “beauty economy” (2)list positive effect (3)list negative effect You should write 160~200 words neatly on ANSWER SHEET 2. 背诵范文： The “beauty economy” actually is “the eyeball economy”. The beauties are used to attract the public attention and make a profit. Meanwhile, the beauty contest activity which we are familiar with is regarded as the most gigantic manifestation of beauty economy. In the supporter’s eyes, the beauty economy gains high business profits through plans, organization, propaganda of the beauty contest. The participants can have the qualifications to participate in the competition as honour. The winners make their social status reach a high position. Thereupon, people become enthusiastic about beauty economy. The merchant has been laughing uproariously which hawked. The beautiful woman has the stage which declares a position. However, others don’t agree with it. Firstly, the beauties are treated as “unliving objects” just like the flower vase, and people pay too much attention to the pretty appearance of the beauties, but their internal world is ignored. Secondly, it leads to the distorted beauty culture. Many girls even women worship blindly the beauties and spend a lot of money in face-lifting to emulate them. Then our traditional aesthetic conceptions are totally overturned, and our conventional virtues completely disappear. Last but not the least, the beauty economy misleads the values. Relying on“being beautiful”, pursuing the wealth, they go after like ducks. And it also causes them to be the money worship.

毕业季向学长学姐讨要考研复习资料的技巧

为学生引路，为学员服务 第 1 页 共 1 页 毕业季向学长学姐讨要考研复习资料的 技巧 毕业季到了，对于很多考研的小伙伴们来说，这个时候绝对是一个向学长学姐讨要复习资料的好时机。但是要提醒大家，在挑选笔记时不要因为一时便宜或是他们的“经验之谈”就是草草购买，我们应该多一些理性，寻找最优性价比。首先要从以下三个问题着手。 一、资料可利用程度 有的考生在买学长学姐的笔记的时候认为有保障，不管三七二十一全部打包带走，其实在选择的时候应该认真挑选，找到自己在复习中真正用的上的才是有价值的。比如上一届考研的前辈们可能在笔记或是专业书上面做了很多标记，密密麻麻的，这可能会妨碍你再一次的复习。因此，建议大家还是自己重新买一套新的书籍，参考着前辈们的笔记自己重新标记，这样才能让自己的思维清晰。其次，大家在选择前辈的参考书时一定要仔细对照你所报院校的参考书目，分清是第几版，作者是谁以及出版社的要求等。随时关注参考书目的变更，以免买到旧版的书籍，影响复习。 二、价钱仔细衡量 大多数考生愿意从上一届考研的学长学姐那里买书是因为二手书比较便宜，同时又能跟前辈们增进感情，讨教经验。这一点当然可以利用，但是大家在买资料时也要多一份理性。通过仔细的挑选衡量一下性价比。虽然是二手资料，但是每年也不乏学长学姐乱要价的现象，所以考研人，一定要感性和理性相结合，擦亮慧眼，货比三家。 三、考试经验适时问 很多同学是本着询问经验才来买资料的，但是经验之谈也要掌握时机和技巧。有些小伙伴们还没有开始专业课的复习就问一些诸如“考研难不难啊”、“专业课最难的地方是什么”等等很笼统的问题，因此很多人会吃闭门羹。认为不是学长学姐们不领情，而是这些问题在初级阶段真的无从回答，只有大家真正的复习到一定的阶段，才能提出更有针对性的问题，这样的答复才是对大家有帮助的。 送走了上一波曾经的考研党， 考研人你们当下要抓住机遇，积累经验。同时也要擦亮慧眼，在购买资料时理性一些，寻找最优性价比。相信大家能够这个过程中更加了解自己的考研方向，摸索到技巧之后，才能大步向前。

考研英语作文范文10篇

考研英语作文范文10篇 范文1 "Good Health" 1．身体健康的重要性。 2．保持健康的途径。 3．我自己的实践。 Good Health The desire for good health is universal. In our competitive society it is important to maintain good health. On the one hand, people with good health can do work with full confidence and their progress in work in turn contributes to their health and happiness. On the other hand, a sick person is usually not interested in everything around him and therefore he loses many opportunities to become successful. There are many ways to keep it. First, those who are always on the go from morning till night should find time to relax because too much stress will affect their health. Second, enough time should be left for sleep because that will help one become rested and refreshed. Finally, regular physical exercises benefit one's health a lot. So one should always keep in mind that a certain amount of exercise is not a waste of time. As for me, I like playing tennis in the morning. I also attach much importance to enough sleep and relaxation. I believe this will ensure my good health for the rest of my life. <评析> 这篇文章语句通顺，语言流畅，句式变化多样，用词面比较宽。就内容来说，则很切题，包括了提纲中的所有要点。第一段的第二句即主题句是从提纲发展而来的，第二段的首句，即主题句也是由提纲中的第二点发展而来。 范文2 Hope Project Education plays a very important role in the modernization of our country. However, because of historical factors, there are still a lot of people in China who are undereducated, especially among youngsters in rural areas. They cannot afford the expenses of schooling and need help. At the same time, China is not able to invest too much money in the matter at present time. It is in this particular situation that the authorities carry out the "Hope Project ". This project is necessary to our country. It is an urgent measure that the government has taken. In the first place, this project will provide conditions for the youngsters to go back to school, which will contribute to their future success. Thus it will lead to the enhancement of the intelligence level in our country. Secondly, education makes it possible for people to acquire knowledge, which is useful to their future work. Hence, this Project benefits the modernization of our country a lot. Finally, it can make more people educated. Therefore, it may indirectly

翻译硕士考研推荐参考书目和资料

翻译硕士考研推荐参考书目和资料【纯个人版本】 考研政治 1.基础：【必买】 肖秀荣1000题，肖秀荣精讲精练 不喜欢肖秀荣官方语言的可以想办法搞到文都考研政治视频的附带讲义进行打印，文都的知识点讲解更加通俗易懂。 2.十月购买文都出品的《形势与政策》小书，其中专题部分特别有用，良心资料。 3.卷子：《真题》《肖八》《肖四》《徐四》 真题主要价值在熟悉选择题难度和保持练习量，肖八肖四尽量做完，肖四按照专题总结全部背完。徐四2017押题牛逼，2018没啥卵用，但是有时间的小伙伴可以尝试背一下主观题，选择题可以不做，没有参考价值。 PS：提供一个背诵方法，将要背的东西按照专题整理录音在手机里，语速保持较慢，一个问题读完之后停顿几秒，这样可以不依靠纸质材料在脑子里形成印象，并且走在路上也可以带着耳机听，贼省时高效。 提醒：不要把运气都押在肖四上，近几年反押题越来越厉害，一般都是压中了考试题目中的材料，而不是准确问题，但是准确的问题也至少能压中三个小问。所以心里要有逼数，即使对党的讴歌再恶心人也得关注别的材料。要特别说明的是，文都的形势与政策那本书专题模块的划线部分非常有用。 4.微博：肖秀荣、蒋中挺 微信公众号：文都考研（这个好）、蒋中挺、肖秀荣、有道考研 翻译硕士英语 1.词汇：刘毅10000、专八词汇、GRE词汇选两本。没时间的选专八或刘毅其中一本。 找一些近义词辨析看 2.单选题材料：专业四级单选（主要是语法和近义词） 以前的英语六级单选，群文件有（主要是词汇） MTI各校英语真题（时间充裕做） 3.完形填空题材料：历年英语一英语二真题 4.改错题材料：专八改错练习，专八历年改错真题 5.阅读材料：根据学校历年真题题型来练习 类似于专八的有选择和问答的做专八阅读真题和专八阅读模拟题，不要买星火，星火出题比较偏。 纯选择的做历年英语一真题和六级真题 6.作文材料： 雅思范文带解析版本，专八作文（推荐冲击波和2012年版本星火范文） 搜集近几年各校出的作文题目，挑选一些搜索是否有相关文章，看完后自己总结再写一遍。 翻译基础 1.专八翻译（偏文学类） 2.跨考黄皮书翻译基础真题及解析 3.张培基第一本，有时间可以看第二本（文学散文类，这两年不是主流，不用背，理解） 4.韩素音翻译大赛历年题目和参考译文，百度文库和群里都有 5.典籍英译文章，自己找

考研高等数学全面复习资料电子版

高等数学考研复习资料，最全篇，适合于一遍，二遍复习研究细节，祝你考研数学春风得意马，突破130分大关！ 目录 一、函数与极限 ········································································错误!未指定书签。 1、集合的概念····································································错误!未指定书签。 2、常量与变量····································································错误!未指定书签。 2、函数·············································································错误!未指定书签。 3、函数的简单性态······························································错误!未指定书签。 4、反函数··········································································错误!未指定书签。 5、复合函数·······································································错误!未指定书签。 6、初等函数·······································································错误!未指定书签。 7、双曲函数及反双曲函数·····················································错误!未指定书签。 8、数列的极限····································································错误!未指定书签。 9、函数的极限····································································错误!未指定书签。 10、函数极限的运算规则 ······················································错误!未指定书签。

考研英语一小作文真题及范文3篇

考研英语一小作文真题及范文3篇 英语一小作文真题：51.direction You are to write an email to James Cooka newly-arrived Australia professorrecommending some tourist attraction in your city .Please give reason for your recommendation. You should write nearly on the answer/sheet. Dot not sign your own name at the end of the email .use "li ming"instead Do not write the address.(10 points) 参考范文1(网友版)： Dear Prof. James Cook Welcome to China. I know you love tra veling so I’m writing this letter to recommend to you one of my favorite scen I think you must like it for the reasons as follows. To begin with there are an amount of beautiful scenic spots such as the Ice and Snow Kingdom in winter the Sun island the Central Street and so on. In addition you could taste a great number of snacks on the average street. Last but not least the people of Harbin are overwhelmingly hospitable and enthusiastic which is famous all over China. Owing to the reasons discuss ed above I won’t hesitate to recommend this scenic spot to you. I am sure you will enjoy it. Best wishes for you! 【参考范文2(网友版)】 Dear Mr. Cook I am writing this letter to recommend you one of the tourist attractions in my city —The Great Wall. The detailed reasons for my recommendation are listed as the following. At the top of the list the Great Wall is one of the oldest historic interests in China. In addition there are a large number of tourists in China and abroad touring the Great Wall and appreciating its grandness and

考研复习资料word版

第一讲函数、连续与极限 一、理论要求 1.函数概念与性质函数的基本性质（单调、有界、奇偶、周期） 几类常见函数（复合、分段、反、隐、初等函数） 2.极限极限存在性与左右极限之间的关系 夹逼定理和单调有界定理 会用等价无穷小和罗必达法则求极限 3.连续函数连续（左、右连续）与间断 理解并会应用闭区间上连续函数的性质（最值、有界、介值） 二、题型与解法 A.极限的求法（1）用定义求 （2）代入法（对连续函数，可用因式分解或有理化消除零因子） （3）变量替换法 （4）两个重要极限法 （5）用夹逼定理和单调有界定理求 （6）等价无穷小量替换法 （7）洛必达法则与Taylor级数法 （8）其他（微积分性质，数列与级数的性质）

1.61 2arctan lim )21ln(arctan lim 3030-=-=+->->-x x x x x x x x （等价小量与洛必达） 2.已知2030) (6lim 0)(6sin lim x x f x x xf x x x +=+>->-，求 解：2 0303' )(6cos 6lim )(6sin lim x xy x f x x x xf x x x ++=+>->- 72 )0(''06)0(''32166 ' ''''36cos 216lim 6'''26sin 36lim 00=∴=+-=++-=++-=>->-y y xy y x x xy y x x x 362 72 2''lim 2'lim )(6lim 0020====+>->->-y x y x x f x x x （洛必达） 3.1 21)1 2( lim ->-+x x x x x （重要极限） 4.已知a 、b 为正常数，x x x x b a 3 0)2 ( lim +>-求 解：令]2ln )[ln(3 ln ,)2(3 -+=+=x x x x x b a x t b a t 2/300)() ln(23)ln ln (3lim ln lim ab t ab b b a a b a t x x x x x x =∴=++=>->-（变量替换） 5.) 1ln(1 2 )(cos lim x x x +>- 解：令)ln(cos ) 1ln(1 ln ,) (cos 2 ) 1ln(1 2 x x t x t x +==+ 2/100 2 1 2tan lim ln lim ->->-=∴-=-=e t x x t x x （变量替换） 6.设)('x f 连续，0)0(',0)0(≠=f f ，求1)()(lim 2 2 =? ? >-x x x dt t f x dt t f （洛必达与微积分性质） 7.已知???=≠=-0 ,0 ,)ln(cos )(2x a x x x x f 在x=0连续，求a

2010年下学期数学院研究生《泛函分析》复习与练习4答案

2011年下学期数学院研究生《泛函分析》复习与练习4 1、证明 1()l l ∞'=。 （第八章：P229，例题1） 2、设T 是赋范线性空间X 到赋范线性空间Y 的线性算子，若T 的零空间是闭集， T 是否一定有界？ （第八章：P236，#6） 解：令[]0,1X Y ?==，其中[]0,1?是[]0,1上多项式函数全体，视为C []0,1的子空间 T 是X 到Y 的微分算子。若0Tf =，则f 是常值函数。显然常值函数全体是闭子集，但T 是非有界的。（见教材底一节例九） 3、证明：A 是实内积空间X 上的自伴算子时，0A =的充要条件是对所有x X ∈，成立(),0Ax x =。 （第九章：P266，#16） 证明：0A =时。显然结论成立。 反之，对任意,x y X ∈，令V=ax+y ； （AV ，V ）=（A （ax+y ），ax+y ） =2a(Ax,y)=0 由y 的任意性，取Ax=y,则Ax=0； 由x 的任意性知，A=0 （这是参考教材P261，引理1做的） 4、设X 是实内积空间，若222 x y x y +=+，则x y ⊥，当X 是复内积空间时，这个结论是否依然成立？ （第九章：P265，#4） 解 当 X 是实内积空间且 222 x y x y +=+时，由 ()2 2 2 ,2,x y x y x y x y x y ++= +=++得,0x y =即x y ⊥ 在复内积空间上此结论不成立 ，例如0,x y ix ≠=，1x = ()2 ,x y x ix x ix +=++2222 ,,x y i x x i x x x y =++-=+ 但(),,x y x ix i ==-0≠

考研英语作文

What an interesting but ironic/realistic/down-to-ground picture it is! Inside this picture, there ........干货，描述图片，力求准确，不错词。）What really shocked me, after observing the picture , is its intended message that (college students’ poor ability of taking care of themselves 主题句用短语形式，简洁明了写完）is becoming so prevalent in China today that we must attach due attention to it. What has been betrayed in this ironic yet thought-provoking picture is precisely what we are experiencing in contemporary world. In my humble opinion, (student’s inability of taking care of themselves is the inevitable consequenceof必然结果both students themselves and their parents. 总括句，说观点，然后下面分开说For one thing, a number of students take everything in their life for granted. That is why they do not bother to learn some basic life skills. For another thing , their parents’indulgence encourages the laziness of their kids. Some parents are even worse. They even discourage their kids to make efforts to live an independent life. In their minds, children are always the little kids who need consistent love and care.简述观点，分点说，有主次）Considering what has been mentioned above, it is advisable for us to try our best to discourage the phenomenon. At the beginning, effective measures should be introduced to create an atmosphere where it is guarded against its thriving. Furthermore, it is necessary for the education department或者啥啥部门concerned to enhance parents’and children’s awareness of the shortcomings after constantly doing so. Last but not the least, the coordinated efforts, I hope and believe, will surely bring about one desirable result in the forthcoming years. 图表作文 The bar chart and the pie chart (or the line chart or the table) illustrate the main extracurricular activities students commit themselves to and the time they spend on 有啥说啥，用名词形式说. According to the data provided, we can see that students spend 93 minutes daily on doing homework,最大点/最大比例的内容which accounts for the biggest share (39%)百分比of their share time. It is followed by watching TV (46 minutes) and listening to music (34 minutes)次大的，动名词形式, representing 19% and 14% respectively该占多少写多少，没有百分比不写. And one thing that should be paid specific attention to is that students spend least time, only 12 minutes(5%), on doing house chores最小值/最小比例. What has been betrayed in diagrams is exactly what we have seen in modern China. From this finding, it could be easily deduced that students are overwhelmed by the excessive study load, which almost squeezes out their spare time that could otherwise be spent on taking exercise or helping with their family chores写内因. That parents are laying too much emphasis on students’ studies 写原因，一句话can be used to explain why the phenomenon indicated is so prevalent in contemporary China. (That our follow citizens are laying too much emphasis on privately international relationship can be used to explain why corruption is so prevalent in contemporary China.) To address the issue, and to improve the existing extracurricular activities啥结构就写啥structure, schools and teachers are advised to 可以改进的人应该怎样做decrease students’ study load做法, free ing up more time for them to promote physical health and family bounding目的.