问题 选择题
考察下列函数:
①f(x)=sinx-x;②f(x)=|x2-3|-2;③f(x)=2x-x2;④f(x)=lnx-2cosx其中有三个零点的函数是(  )
A.①②B.②③C.③④D.①④
答案

解:∵sinx-x=0∴sinx=x

令y1=sinx,y2=x

根据这两个函数的图象在同一个坐标系中的位置关系知,两个图象有一个公共点坐标原点,

∴原函数的零点的个数是1,故①不正确

|x2-3|-2=0则|x2-3|=2结合图象可知有四个交点,故②不正确

2x-x2=0即2x=x2结合图象可知有3个交点,有两正根2和4和一负根

lnx-2cosx=0即lnx=2cosx,结合图象可知有3个交点

故选C.

单项选择题
问答题

It is hard to predict how science is going to turn out, and if it is really good science it is impossible to predict. If the things to be found are actually new, they are by definition unknown in advance. You cannot make choices in this matter. (46) You either have science or you don’t, and if you have it you are obliged to accept the surprising and disturbing pieces of information, along with the neat and promptly useful bits.
The only solid piece of scientific truth about which I feel totally confident is that we are profoundly ignorant about nature. Indeed, I regard this as the major discovery of the past hundred years of biology. It is, in its way, an illuminating piece of news. (47) It would have amazed the brightest minds of the 18th century Enlightenment to be told by any of us how little we know and how bewildering the way ahead seems. (48) It is this sudden confrontation with the depth and scope of ignorance that’ represents the most significant contribution of the 20th century science to the human intellect. In earlier times, we either pretended to understand how things worked or ignored the problem, or simply made up stories to fill the gaps. Now that we have begun exploring in earnest, we are getting glimpses of how huge the questions are, and how far from being answered. Because of this, we are depressed. (49) It is not so bad being ignorant if you are totally ignorant the hard thing is knowing in some detail the reality of ignorance, the worst spots and here and there the not so bad spots, but no true light at the end of the tunnel nor even any tunnels that can yet be trusted.
But we are making a beginning and there ought to be some satisfaction. There are probably no questions we can think up that can’t be answered, sooner or later, including even the matter of consciousness. (50) To be sure, there may well be questions we can’t think up, ever, and therefore limits to the reach of human intellect, but that is another matter. Within our limits, we should be able to work our way through to all our answers if we keep at it long enough, and pay attention.