用导数新解一类最值问题

目前,高等数学教材中都没有介绍开区间或者半开半闭区间、无穷区间上连续函数的最值或者有有限个间断点的函数的最值问题。文章给出了开区间（a,b）或半开半闭区间（a,b]或[a,b）上连续函数的最值,同时给出了无限区间（（-∞,+∞）,（-∞,a）,（-∞,a],[b,+∞）,（b,+∞））上连续函数的最值以及有有限个间断点的函数最值的求法。     

闭区间上连续函数的性质定理及微分中值定理的推论

本文给出了闲区间上连续函数的性质定理--零点定理,介值定理,微分中值定理--罗尔定理,拉格朗日中值定理的推论及其证明,将函数在闭区间上连续的条件改为在开区间内连续且极限存在(或为∞)的条件,从而拓宽了定理的应用范围.     

开区间上最值问题的探讨及应对策路

人教B版教材在“利用导数研究函数的最值”这一章节中谈到了“最值定理”,即“闭区间上的连续函数在该区间上一定有最大值和最小值”,关于这个定理教材中是这样表述的“假设函数y=f（x）在闭区间[a,b]上的图象是一条连续不间断的曲线,则该函数在[0,b]上一定能够取到最大值和最小值”．在实际解题中我们往往会碰到在开区间上求最值的情况,那么,最值定理在开区间上是否还成立呢？显然是不成立．对此,就有了一些需要我们特别注意的问题．     

连续函数最大值、最小值求法之补充

求一个函数的最大值和最小值,首先要判断其是否存在,然后才可进行求解。现行的微积分教材已对闭区间上连续函数的最大值、最小值问题作了详细论述,本文拟对其它几种情形下连续函数的最大值、最小值问题进行讨论和补充。 一、开区间(a,b)内连续函数的最大值和最小值问题 结论1 若函数f(x)在(a,b)内严格单调,则f(x)在(a,b)     

关于一元非连续函数黎曼可积性的讨论

本文的主要工作是,用较初等的知识对一元非连续函数的黎曼可积性作一些讨论。引理1 设函数f(x)定义在闭区间[a,b]上,且在(a,b)内每一点ξ,f(ξ-0)和,f(ξ+0)都存在,在区间的端点,f(a+0)、f(b-0)存在,则对任给>0,在(a,b)内只存在有限多个ξ满足     

微分中值定理的一种推广

如果函数f(x)在闭区间[a,b]上连续,在开区间(a,b)内除有限个点的导数为 ∞和-∞外,其它点的导数都存在,那么在(a,b)内至少有一点ξ(ξ∈(a,b)),使得函数在该点的导数f'(ξ)=f(b)-f(a)/b-a.     

开区间上的连续函数与可积的关系

在数学分析中,有我们已经熟知的结论:闭区间上的连续函数一定可积.但对于开区间上的连续函数有没有类似的性质呢?本文探讨了有限开区间上连续函数的性质,有限开区间上函数可积的充分条件,得出了开区间上连续函数可积的充要条件.     

函数一致连续与连续的关系讨论

函数f（x）在区间I上一致连续,可得f（x）在区间I上连续,反之不一定．若I为有限闭区间[a,b],据Cantor定理,f（x）在[a,b]上连续等价于f（x）在[a,b]上一致连续．通过几个具体例题的证明,探讨了开区间以及无穷区间上一致连续与连续的关系．     

关于连续函数最值问题的补充

讨论了开区间和半开半闭区间上连续函数的最值问题,获得了一系列最大值、最小值的存在性结果以及相应求法.     

用Lebesgue方法证明单元函数的一致连续性定理

有限闭区间上的连续函数,其基本定理中的介值定理、有界性定理和一致连续性定理,在多数教材中,常采用反证法或Borel有限覆盖定理加以证明。M·Spivak在其教材中,用Lebesgue方法证明了介值定理和有界性定理。本文说明:运用Lebesgue方法可以证明一致连续性定理。定理设f(x)在有限闭区间[a,b]上连续,则f(x)在[a,b]上一致连续。证明任意给定ε>0,作集合     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.     

Improvement of one-cycle controller by use of proportional integral differential controller

1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec…     

库克斯顿城堡

城堡, 是欧洲典型的建筑之一, 每个城堡都有一个美丽的传说或是一段历史。从本期开始, 我们将推出“城堡之旅”, 带各位读者去浏览、观赏欧洲各地的城堡, 开始一段文化与历史的旅途!     

The Reader Response Approach to Teaching of English Literature

During interview with English majors, it was found that a majority of students expressed disappointment with their experience of English literature classes. Students' dislike of learning English literature appears to be the major problem of teaching English literature in China. Reader response approach is a good way to solve this problem. In this paper, I explain the rationale behind the reader response approach, such as its origin, definition, features, assumptions, and strategies. Then I illustrate how reader response approach works as a teaching strategy by presenting several teaching models. At last I evaluate its usefuiness for teachers and present the advantages of reader response approach in Chinese context.