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问题 解答题
利用函数的单调性定义证明函f(x)=
x
x-1
，x∈[2，4]是单调递减函数，并求函数的值域．
答案

证明：在[2，4]上任x1，x2．x1＜x2，f（x1）=

x1
x1-1
，f（x2）=
x2
x2-1

∴f(x1)-f(x2)=

x1
x1-1
-
x2
x2-1
=
x2-x1
(x1-1)(x2-1) 

∵2≤x1＜x2≤4，∴x2-x1＞0，x1-1＞0，x2-1＞0

∴f（x1）-f（x2）＞0，

∴f（x1）＞f（x2），∴f（x）是在[2，4]上的减函数

当x=2时函数取最大值2，当x=4时函数取最小值

4
3

 因此，函数的值域[

4
3
，2]．

填空题

用所给动词的正确形式完成短文。

Dear Zhang Lin,

     How's it going? I    1   (have ) some problems at school. I find it difficult to work in the evening and I

can't concentrate on anything at the moment. I spend most of my time     2   (listen) to records or watching

TV instead of doing my homework.The other students in my class    3   (be) much better than me.I have the

following problems as well. I can't always take down the important things my teacher    4   (say), because

I write too slowly, She    5    (tell) me that I'm falling behind my classmates in my studies. I'm not good

at     6   (write) and I usually hand in my homework late because I won't do it until the last minute. So I often

have to find different excuses   7    (let)my teacher know why I haven't done the homework. I'm sure I    8  

(get) through my final exam in January. I'm now so far behind the other students that I don't know how I

can    9    (catch) up with them. Last week, when my teacher    10  (help) me with my homework, she found

so many mistakes, which made me more upset.

      Could you please give me some good suggestions?

                                                                                                                                                  Yours, 

                                                                                                                                                  Wei Hua.

1._______ 2._______ 3._______ 4._______ 5._______

6._______ 7._______ 8._______ 9._______ 10._______
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问答题 简答题

简述三废防治的措施有哪些？
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