例说寻找原型解数学题

本文试用寻找原型的思想来解决一些与抽 象函数有关的周期问题，供参考． 例１已知函数ｆ（ｘ）满足ｆ（ｘ＋ａ）＝ （ａ为常数，且ａ≠０），求证：函数 １－ｆ（ｘ） ｆ（ｘ）是周期函数． 分析：观察式子的特点，易知函数ｆ（ｘ）的 原型是ｙ＝ｔｇｘ，且ｔｇ（ｘ＋）＝，而４ × ＝π正是函数ｙ＝ｔｇｘ的周期，故我们可以猜 测４ａ为函数ｆ（ｘ）的周期． 证明：ｆ（ｘ＋２ａ）＝ｆ［（ｘ＋ａ）＋ａ］＝ １－ｆ（ｘ＋ａ） ｆ（ｘ＋４ａ）二ｆ［（ｘ＋２ａ）＋２ａ］＝ 即ｆ（ｘ＋４ａ）＝ｆ（ｘ），所以函数ｆ（ｘ）是周 期函数． 例２…     

浅谈分段函数

浅谈分段函数舒元生（湖南省祁东县四中４２１６８１）函数ｙ＝｜ｘ｜（ｘ∈Ｒ）与函数ｙ＝ｘ（ｘ≥０）－ｘ（ｘ＜０）｛是同一函数，不过后者称为分段函数．由此可知，分段函数不是几个函数，而是同一个函数，只是为了解决问题的需要，才将它分为几个式子来表示罢了．例...     

函数f（x）＝x＋1x的一个应用

函数ｆ（ｘ）＝ｘ＋１ｘ的一个应用雷正才（湖南省娄底一中４１７０００）我们知道，利用函数的单调性可以比较有关数值的大小，因而利用函数的单调性可以证明有关不等式．下面举几例说明在不等式的证明中函数ｆ（ｘ）＝ｘ＋１ｘ的应用．命题函数ｆ（ｘ）＝ｘ＋１ｘ在区间...     

关于导函数的一个特性

关于导函数的一个特性任建娅函数ｆ（ｘ）在ｘ０点的导数ｆ＇（ｘ０），从导数的定义来讲，从导函数ｆ＇（ｘ）出发，那么ｆ＇＋（ｘ０）与之间有什么区别，又有什么联系呢？下面就以ｆ＇＋（ｘ０）与ｆ＇（ｘ０＋０）为例来讨论这个问题。１ｆ＇＋（ｘ０）与ｆ＇（ｘ０＋...     

x＝f~（－1）（y）与y＝f~（－1）（x）是同一函数吗

ｘ＝ｆ~（－１）（ｙ）与ｙ＝ｆ~（－１）（ｘ）是同一函数吗庆阳一中白惠敏函数ｘ＝ｆ－１（ｙ）与ｙ＝ｆ－１（ｘ）是否表示同一函数？部分学生往往搞不清楚。为此，在教学中可引导学生深入理解函数概念，进一步掌握“函数概念是从定义域Ａ到值域Ｂ的映射”，决定函数的...     

函数方程的几种解法

函数方程的几种解法李品贤中学阶段的函数方程的一般解法，有以下几种：一、解方程（组）法，也称为变量代替法。例１．设ｆ（Ｘ）是定义在Ｒ上的函数且满足：ｆ（２ｘ—３）＝ｘ２＋ｘ＋１，求ｆ（ｘ）。解：设ｔ＝２ｘ－３，则由ｆ（２ｘ—３）＝ｘ２＋ｘ＋１，得所求函...     

代数函数的最值问题的图象解法

求各种函数的最值问题是中学阶段的重点与难点．中学阶段所涉及到函数通常是二元函数ｆ（ｘ，ｙ）或带着约束条件的二元函数ｇ（ｘ，ｙ），若令ｆ（ｘ，ｙ）＝Ａ或ｇ（ｘ，ｙ）＝ｍ，则可以在ｘＯｙ平面上画出其图象，利用函数图象来求解最值问题是一种常用的方法，其中典型的例子是二次三项式的最值问题．     

函数对称性的一个定理及应用

函数对称性的一个定理及应用安徽省泾县中学汪民岳函数的对称性，是函数一个重要性质，有着广泛应用．下面介绍一个简洁优美的对称定理：函数ｙ＝ｆ（ｘ）关于ｘ＝ａ对称ｆ（ａ＋ｘ）＝ｆ（ａ－ｘ）ｆ（ｘ）＝ｆ（２ａ－Ｘ）．（以下简记）证明从略．下面举例说明应用．一...     

一元函数的Lipschitz连续与一致连续及可微的关系

一元函数的Ｌｉｐｓｃｈｉｔｚ连续与一致连续及可微的关系任建娅为了论述方便，首先给出定义：定义，若函数ｆ（ｘ）在区间Ｉ有定义，有｜ｆ（ｘ）－ｆ（ｙ）｜≤Ｌ｜ｘ－ｙ｜，其中Ｌ是常数，则称函数ｆ（ｘ）在区间Ｌｉｐｓｃｈｉｔｚ连续。函数ｆ（ｘ）在区间ＩＬｉｐ...     

Gauss求积公式的误差分析

本文考虑利用Ｇａｕｓｓ求积公式Ｑｎ（ｆ），ｎ∈Ｎ来逼近定积分Ｉ（ｆ）＝ｗ（ｘ）ｆ（ｘ）ｄｘ。其中权函数ｗ（ｘ）＝Ｗ（ｘ）／ｐ（ｘ），ｐ（ｘ）＝（２ｂ＋１）ｘ２＋ｂ２，ｂ＞０和Ｗ（ｘ）＝（１－ｘ）α·（１＋ｘ）β＝，α，ｎ＞１。误差函数Ｒｎ（ｆ）＝Ｉ（ｆ）－Ｑｎ（ｆ），在某些解析函数空间是连续的。对于满足限制条件的权函数，我们得到了计算误差函数Ｒｎ（ｆ）的明显表达式。若α＝β＝和ｎ＞１时，若和α＝β＝和ｎ＞１时，若和α＝－β＝和ｎ＞２时，     

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?     

汉字倒说

汉字的六书,《说文》对“转注”一类,语焉不详。后世学者提及转注,也仅限于许慎所举出的例字。《汉字例说》一文,作者从转注的角度综合考虑,对部分现代常用字作了分析,跟传统的解释有所不同。希望能抛砖引玉,互相切磋,以推进学术研究。     

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.     

钱生钱!

我们绝大部分人都同意一件事情——我们喜欢金钱。但是你对金钱的喜欢之情足够到让你创立一份事业么?.财富通常被人忽视,主要在于人们不能真正了     

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!     

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.