题目

已知函数 (为实常数) ． （1）当时，求函数在上的最大值及相应的值； （2）当时，讨论方程根的个数． （3）若，且对任意的，都有，求实数a的取值范围． 答案：1），当时，．当时，又，故，当时，取等号……3分 （2）易知，故，方程根的个数等价于时， 方程根的个数。 设=，当时，，函数递减，当时，，函数递增。又，，作出与直线的图像，由图像知： 当时，即时，方程有2个相异的根； 当 或时，方程有1个根； 当时，方程有0个根；……………8分 （3）当任务型阅读 阅读短文，根据短文内容完成表格中所缺信息，每空限填一词。Hobbies are activities, which we do in our free time. There are so many kinds of hobbies one can choose for his or her own. Some hobbies are really expensive, and some are even dangerous.The most popular hobbies in our country are as follows:Collecting hobbies We can collect a lot of things. Usually people collect the stamps, postcards or coins. Some people collect unusual things like old cars, old motorbikes or other interesting things, which could be very expensive.Art hobbies Going to the theatre, concert（音乐会）, opera; playing some instrument ( the most popular instrument is guitar ); painting, writing, poetry. There are many clubs—such as singing, dancing, etc.Sports games Everybody do some sport activities—sport can keep us fit. Many students are members of a sports club—basketball, volleyball or swimming.The other popular hobby is watching TV or a video, playing computer or video games, but it is not so good for your eyes and your mind. Many people here like to spend their free time reading books, magazines and newspapers. Some people like listening to music better. Going out can be very expensive now.Many students would like to make use of their hobbies in their future jobs, e.g. working with computer, but it is not so easy. Hobbies are very important for everybody. A man would be very poor without a hobby and would not be pleased.Title 1. for Us to Choose FromIntroduction ?There are many hobbies one can choose: expensive or dangerous.Main bodyCollecting hobbies?Many people like 2. stamps, postcards or coins.?Some people like to collect things, such as old cars, old motorbikes, etc.Art hobbies?We can go to the theatre, concert or opera.?We can also learn to play some instrument.?Some have 3. painting, writing or poetry.?Going to clubs for entertainment（娱乐）is also very interesting.Sports games?We can take part in some sports activities or4. sports clubs.Other hobbies?Watching TV or a video and playing computer or video games are interesting things to do, but not too much, for they may be bad for our eyes and mind.?We can choose to read or enjoy music for pleasure.Conclusion ?For many students hobbies are 5. for their future jobs.?Hobbies are important for everyone, without which we would be poor and not pleased.