分类 我的随笔 下的文章 - 我的学记|刘航宇的博客

补充:情态动词的用法 四 补充：情态动词的用法什么是情态动词？表示说话人主观态度的词，情态动词后加动词原形。情态动词表对现在和将来的推测。用法1） 情态动词表示对现在和将来的推测你一定很有钱。他是一个男孩吧。2） 情态动词表示对过去的推测举例• 他大学的时候一定很自卑吧。He must have been self biased in his university.• 你本没必要以这种方式向我表达爱。You neednot have shown your love in this way.• 我本能够成为一名优秀的诗人。I could have become a prominent poet.• 如果有机会的话，我们本应该结婚了。We should have got married if there exists achance.must have been一定做过某事 must not禁止做某事 can’t其否定neednot have …没必要做某事但是做了 could have …本能做某事，但确没有做，表遗憾。I could have lent you some money五 插入语放在句子中间，通常是定语状语，同位语，用逗号、破折号隔开

虚拟语气特殊用法及考点分析 虚拟语气特殊用法1）以下情况从句用“should + v原型.”表示虚拟，并且 should 可以省略。以防in case,lest,forfear that命令order,direct,command建议advise,suggest,propose要求ask,request,demand,require用虚拟是必要的举例• 以防得传染病，你最好呆在家里。In case that you should develop fatal infections,you had better stay at home.• 我应该参加更多的活动是非常重要的。It seems crucial that more activities should be attended show myself.• 老师要求我们交研究报告。The teacher asks that we should had2） 以下情况从句用过去时表示虚拟常见的有两个：would rather 和 It is high time that…举例• 是时候培养孩子的独立性了。The independence of kids should were cultivated by senior citizens.3） 以下情况要区别对待把本来的时态变成相应的过去时就行了。常见的词有：wish; if only; but for; or/otherwise; as if/as though 等举例• 如果我是你的孩子该多好啊。If only I were your child.If only I had been your child.考点分析1） 写作举例• 对于普通市民来说，保护小区环境，不乱丢垃圾是非常必要的。It is important that the community environment should be protected and rubbish be never dumped for the common.2） 长难句分析虚拟语气和非虚拟语气都是直接翻译练习• If that happened, passionate consumers would try to persuade others to boycott products, putting the reputation of the target company at risk.如果这种情况发生，激情的消费者会尝试劝说其他人，抵制这种产品，使目标公司荣誉受到破坏。• The millions of calculations involved, had they been done by hand, would have lost all practical value by the time they were finished.如果用手工计算，等他们结束时候，所涉及的数百万次计算将会失去他的存在价值

微分4大中值定理 罗尔中值定理条件：（1）f(x)在[a,b]连续。（2）f(x)在(a,b)可导。（3）f(a)=f(b)。结论：在a和b之间必有一个值ξ使得f’(ξ)=0。几何意义：在该条件下的函数，必可在在其区间内找到一点使得切线斜率为0。引申---费马引理y=f(x)，若x0为y=f(x)的极值点，则f’(x0)=0。 拉格朗日中值定理条件：（1）f(x)在[a,b]连续。（2）f(x)在(a,b)可导。结论：在a和b之间必有一个值ξ使得f’(ξ)=(f(b)-f(a))/(b-a)。几何意义：在该条件下的函数，必可在其区间内找到一点使得切线斜率与端点连线斜率相等。拉格朗日中值定理是罗尔中值定理的推广。证明：使用曲线减去两端点连线得出一个函数，再对该函数应用罗尔中值定理。使用该定理的信号：要求证的式子中有一个端点处函数值之差。柯西中值定理条件：（1）f(x)、g(x)在[a,b]连续。（2）f(x)、g(x)在(a,b)可导。且g’(x)≠0结论：在a和b之间必有一个值ξ使得(f'(ξ))/(g'(ξ))=(f(b)-f(a))/(g(b)-g(a))。柯西中值定理是拉格朗日中值定理推广。证明：使用参数方程，将f(x)和g(x)作为参数表示。证明过程与拉格朗日中值定理相同。使用该定理的信号：要求证的式子中有两个端点处函数值之差。泰勒中值定理泰勒中值定理即带有拉格朗日余项的泰勒公式。拉格朗日中值定理是带有拉格朗日余项的泰勒中值定理的特例。使用该定理的信号：高阶导数。使用方法：（1）确认n的取值，一般根据高阶导数的阶数选取。（2）确认x0的取值，一般选取题中已知导数值的点。（3）确认x的取值，一般为题中所给已知值的点或端点和极值点。

虚拟语气 什么是虚拟语气？虚拟语气表示与事实相反或语气委婉。只需要把句子时态变成过去式，则为虚拟语气一般用法If引导的条件状语从句举例• 如果你是我眼中的一滴泪，我永远不会把它流出来。If you are（were） a tear in my eyes,I will(would) never shed it • 如果昨天晚上我是一条狗，我就可以和你们睡在床上了。If I was(had been过去的过去) a dog,I could sleep（have slept） with you?虚拟语气中be过去式只有were没有was,could=would=might

英语的特殊结构 综合练习• 教师节就要来了，我借这次机会向给予我帮助的老师表示衷心的感谢。Teacher’s day approaching,I express my sincere appreciation to teachers who have given me assistance by the chance.• 生命很短暂这个事实已经被很多人接受了。The truth has been accepted by the mass that life becomes so short that every day should be valued.• 上课不集中精力而又希望通过考试的学生，往往会发现结果不令人满意。Students who fail to concentrate in class but wish to pass examinations perceive perceive that the consequence proves less impressive• 为了实现我的梦想，我一直在思考我应不应该和男朋友分手。I in order to realize my dream am considering whether I should depart with my boy friend.• 在有学校的地方，司机应该缓行。Where there exists a school,drivers should go slouly— 强调句型It is (被强调)….that主要/who/which构成举例• 我昨天在街上遇到了我的旧情人。• I met my old flame in the street yesterday.改为强调句：It was I that met my old flame …….强调句型可以强调句子所有成分，唯一不能强调谓语。练习• 为了实现我的梦想，我一直在思考我应不应该和男朋友分手。It is to realize my dream that I am ….• 有很多的原因可以解释这种现象。There remain abundant elements to account for the issue.考点分析1） 写作中的应用所有句子都可写成强调句练习• 你至今仍然没有意识到就是因为你交友不慎，你才没有考上心目中理想的大学。So far,you have never realized that because you have unforable friends,you failed to …• 就是在我的女儿出生以后，我才意识到母亲的伟大。2） 长难句分析练习• But it is the arrival of new satellite channels—funded partly by advertising andpartly by viewers’ subscriptions—that will bring about the biggest changes in the long term.• Perhaps it is humankind’s long suffering at the mercy of flood and drought that makes the idea of forcing the waters to do our bidding so fascinating.二 倒装什么是倒装？倒装就是把一句话写成一般疑问句形式，也就是给一句话加个助动词或把be动词放在句首举例• 你爱我吗？Do you love me?• 你去过欧洲吗？Have you been to you europe• 你爸爸是个老师吗？Is you father a teacher.倒装的具体用法1） 否定词放在句首用倒装I can hardly speak JapaneseHaredly can I …….举例• 我几乎不会说日语。• 我绝对不会爱上你。I by no means love you.By no means do l love you.• 玩手机不但影响年轻人的身心健康，而且浪费了他们的时间。Playing phones not only influences the physical and mental health of youngsters but also waste their precious timeNot only does plying influences倒装的考点分析1） 写作中的应用举例• 文化交流不但能促进我们国家经济的发展，而且还能开阔个人的眼界。Not only can cultural exchange promote economic advance but also makes our egesiht broad.• 我累得浑身都没有劲了。I am so exhausted that I have no energy throughout• 当外面下雨的时候，只有在自己的家里，我才感到安全和放松。Only at home do I feel safe and relaxed.2） 长难句分析还原倒装部分后再翻译练习• Television is one of the means by which these feelings are created and conveyed—and perhaps never before has|| it served so much to connect different peoples and nations as is the recent events in Europe.

比较结构的特殊用法(英语) as 专题as 意思总结• 1.as+ n. 作为• v. + … + as as意思取决于前面名词• as + 句子 当…时候，定语从句，认为状语，句意分析。练习• As作为 a logical合理 consequence of this development, separate分开 journals have now appeared aimed mainly towards either professional or amateur readership.• As a result, the support主语 for ambition as a healthy impulse, a quality to be admired and fixed in the mind of the young, is谓语 probably lower than it has ever been in the United States.• I shall define定义 him as an individual who has elected as his primary duty and pleasure in life the activity of thinking in a Socratic（苏格拉底的） way about moral problems.• Tylor defined culture as “...that complex whole (which includes belief, art, morals, law, custom, and any other capabilities and habits acquired by man as a member of society.”)• As is true of any development society发达国家, in America a complex set of cultural signals, assumptions假设, and conventions underlies all social interrelationships.关系• Shortlists for job interviews, election ballot papers, lists of conference speakers and attendees: all tend to be drawn up alphabetically, and their recipients lose interest as当…时候 they plough through them.• With other audiences you mustn’t attempt to cut in with humor as they will resent an outsider making disparaging remarks about their canteen or their chairman.• New forms of thought as well as new subjects for thought must arise in the future as就像 they have in the past, giving rise to new standards标准 of elegance优雅.than 专题1） not so much as = not even 甚至不/没有举例• He cannot so much as spell a word.他甚至不能拼写一个单词• He did not so much as ask me to sit down.他甚至都没邀请我坐下。2） not so much A as B 与其说 A 倒不如说 B举例• He is not so much a teacher as a poet. • 与其说他是老师，不如说他是诗人• 3）more A than B • 与其说 B 不如说 A举例• He is more a poet than a teacher.4） more than…• 后加名词• Liu more than is a teacher.• 翻译：不仅仅是• 后加形容词/副词• 翻译：非常的• 后加数词• 翻译：多余

句子所有成分大总结练习 举例• 我妈妈是一个美丽的女人。My mother is an elegant lady=My mother is a lady of elegance.=my mother is a lady as elegant as a lily.=my mother is a lady looking as elegant a lady=….. who looks as elegant as a lady.• 她杀死了她的老公。She killed her husband with a sharp knife.=she applying a sharp knife,keilled her hushand.=when she applied a shar knife,she keiied her hushand.• 我遇见你是我的荣幸。That I met you is my honor.Meeting you is my honor.• 我的梦想是通过研究生考试。My dream is to pass the examination of post gradutes.My dream is that I pass the examination of post gradutes.英语长难句的模样：(状 )，主语（定/同/状）谓语 宾语（定/同/状）.练习：拉长句子• 英语很重要。English (a universal language throughout the world)is vital (although it is hard to recite these words)• 我要给你推荐一个旅游景点。I (a graduate in this university) will recommend you a tourist attraction which kepps popular Chinese travelers.• We are singing songs.

微积分不等式的证明方法[高等数学] 证明方法总结：（1）利用函数单调性证明不等式若在（a,b）上总有f（x）的导数大于零，则函数f（x）在区间(a,b)上单调增加；若在（a,b）上总有f（x）的导数小于零，则函数f（x）在区间(a,b)上单调减少。（2）利用拉格朗日中值定理证明不等式对于不等式中含有f（b）-f（a）的因子，可考虑用拉格朗日中值定理先处理一下。扩展：拉格朗日中值定理条件：（1）f(x)在[a,b]连续。（2）f(x)在(a,b)可导。结论：在a和b之间必有一个值ξ使得f’(ξ)=(f(b)-f(a))/(b-a)。几何意义：在该条件下的函数，必可在其区间内找到一点使得切线斜率与端点连线斜率相等。拉格朗日中值定理是罗尔中值定理的推广。证明：使用曲线减去两端点连线得出一个函数，再对该函数应用罗尔中值定理。使用该定理的信号：要求证的式子中有一个端点处函数值之差。（3）利用函数的最值证明不等式若函数f（x）在闭区间[a,b]上连续，则f(x)在区间[a,b]上存在最大值M和最小值m.（4）利用泰勒公式证明不等式如果要证明的不等式中，含有函数的二阶或二阶以上的导数，一般通过泰勒公式证明不等式。不等式证明的难点也是辅助函数的构造，一般可以通过要证明的不等式分析得出要构造的辅助函数。扩展： 泰勒公式泰勒公式中系数表达式：(f^((n) ) (x_0 ))/n! (x-x_0 )^n 当x_0=0的时候，泰勒公式则称为麦克劳林公式。

状语和状语从句的考点分析 一 写作中的使用作文中任何一句话旁边都可加一个状语把句子拉长。举例• 我爱你。I love you very muchI love you for my whole life.• 你可以像猪一样生活，但是你永远不会像猪一样快乐。one can live as if he were a pig conversely he can never be as delighted as a pig.二 长难句分析能快速识别状语，并通顺的翻译出来如何识别状语呢？只要句子中见到以下，一定为状语：副词：比较、条件、结果、原因、让步、目的、方式、伴随分析长难句 n+时间/地点，需要区别状语、定语I love a boy in Zhejiang University.我爱浙江大学男孩如果无法确定定语或状语话，定语优先。只有定语翻译“明显”不成，则状语。练习• ，The Greeks主语 assumed认为谓语 that宾语 the structure of language had some connection with the process of thought, [ which took root( in Europe)地状( long before people realized how diverse languages could be.) 时状] 定语• Social science is谓语 that branch分支 of [intellectual enquiry/定1 which seeks to study humans and their endeavors/2 (in the same reasoned, orderly, systematic, and dispassioned manner)状语 that natural scientists use for the study of natural phenomena/3.]定语• The behavioral sciences have been(谓语) slow to change partly 原因状语because the explanatory items often seem to be directly observed and partly原因状语 because other kinds of explanations have been hard to find.• Traditionally, legal learning has been viewed (in such situations)装 as the special preserve宾语 [of lawyers]定, rather than而不是 a necessary part宾语 of the intellectual equipment of an educated person.• (While虽然 it is easy to ignore （in our contact with them） the effect of our acts upon their disposition)让步状语, it is（主句谓语） not so easy (as in dealing with adults.)状语从句动词不定式当主语，通常放于句末，加it做形式主语,It形式主语。五 句子所有成分大总结主干成分：主语、谓语、宾语、表语（主语解释者）修饰成分：同位语（解释n）、定语(修饰n)、状语(修饰除n)、补语(补充宾语)

【高数】常用不定积分公式及其应用 1、∫ a dx = ax + C，baia和C都是常du数2、∫ x^zhia dx = [x^(a + 1)]/(a + 1) + C，其中a为常数且dao a ≠ -13、∫ 1/x dx = ln|x| + C4、∫ a^x dx = (1/lna)a^x + C，其中a > 0 且 a ≠ 15、∫ e^x dx = e^x + C6、∫ cosx dx = sinx + C7、∫ sinx dx = - cosx + C8、∫ cotx dx = ln|sinx| + C = - ln|cscx| + C例如：x/(1+x)^2的的不定积分=[(1+x)-1]/(1+x)^2=1/(1+x)-1/(1+x)^2换元t=1+x=(1/t) dt - t^(-2)dt积分得到ln|t|+1/t+C=ln|1+x|+1/(1+x)+C

【高数】极限中常用等价无穷小 求极限时，使用等价无穷小的条件：被代换的量，在取极限的时候极限值为0；被代换的量，作为被乘或者被除的元素时可以用等价无穷小代换，但是作为加减的元素时就不可以，加减时可以整体代换，不一定能随意单独代换或分别代换替bai换公式如下 :

方式、条件、比较状语从句 方式状语从句常见的引导词• as• the way• as if / though从句做状语• by/through/by means of• in…way/manner介词短语做状语举例• 她看起来就像冰做的一样。She looks as if she were made of ice条件状语从句引导词• suppose that• supposing that• if• unless• provided that• as long as• so long as举例• 只要有一丝希望，我也不会放弃。If there seems a ghost of hope,I will never give up.比较状语从句引导词• as…as• than举例• 你像我一样漂亮。You are as beautiful as me.错误You are as beautiful as I （am beautiful）省略部分