问题 解答题

用定义证明函数f(x)=x2+2x-1在(0,1]上是减函数.

答案

证明见试题解析.

题目分析:证明一个函数为减函数,根据定义设为所给区间上的任意两个实数,且,然后作差,但一定要注意的是,对差,我们一般是进行因式分解,把它变成几个因式之积,实际上是要得到几个容易判断正负的因式之积,从而很快可以得出差是正是负.

试题解析:证明:设,则

∴函数上是减函数.

阅读理解

What’s the difference between the British Isles, Britain, the United Kingdom and England?

The British Isles is made up of two large islands: One is called Ireland and the other Britain. Britain, or Great Britain, is the larger of these two islands and it is divided into three parts: Scotland, Wales and England.

The United Kingdom (UK) is short for the United Kingdom of Great Britain and Northern Ireland. It is made up of Scotland, Wales, and England (i.e. the whole of Britain), and also about one-sixth of Ireland, the Northern part. The rest of Ireland is self-governing(自治的).

England is the largest, most populous (人口众多的), and generally speaking, the richest section. English people often use the words “England” and “English” when they mean “Britain” and “British”. This sometimes makes the Scots and the Welsh angry. The Scots are very proud of their separate nationality. The Welsh too do not consider themselves as England, and have a culture and even a language of their own. Ireland became part of the United Kingdom in 1801, but is soon grew discontented (不满的), and for forty years the “Irish Question” was the greatest headache of British Parliament(国会). At last, Ireland divided itself into two: Northern Ireland remained loyal(忠诚于) to the Crown(英国王室), and in 1922 the rest of the country broke away to form Irish Free State, now the Republic of Ireland.

小题1:Which is the largest in area?

A.The British Iles

B.Great Britain

C.England

D.The United Kingdom小题2: Which is the largest island of the British Isles?.

A.Ireland

B.Britain

C.England

D.Northern Ireland小题3:The United Kingdom is mainly made up of          .

A.3 parts: Scotland, Wales, and England

B.4 parts: Scotland, Wales, England and Ireland

C.2 parts: the whole of Britain and Ireland

D.2 parts: the whole of Britain and Northern Ireland小题4: Strictly speaking(严格地说), which is wrong?

A.“English” refers(指) to people of England.

B.“The Scots” refers to people of Scotland.

C.“England” refers to all the people to the UK.

D.Only one-sixth of Ireland belongs to the UK.小题5:Who will be happy if we use “England” when we mean Britain?

A.The British

B.People of England

C.People of the Republic of Ireland

D.The welsh

单项选择题