问题 填空题
函数f(x)=
x2+ax
(x+1)(x-1)2
为奇函数的充要条件是a=______.
答案

必要性:因为函数f(x)=

x2+ax
(x+1)(x-1)2
为奇函数,则f(-x)=-f(x)

(-x)2+a(-x)
(-x+1)(-x-1)2
=-
x2+ax
(x+1)(x-1)2

∴f(-2)=-f(2)

(-2)2+a(-2)
(-2+1)(-2-1)2
=-
x22+2a
(2+1)(2-1)2

解得a=-1;

充分性:当a=-1时,f(x)=

x2-x
(x+1)(x-1)2
=
x
(x+1)(x-1)
,此时满足f(-x)=-f(x),

故函数f(x)=

x2+ax
(x+1)(x-1)2
为奇函数.

∴函数f(x)=

x2+ax
(x+1)(x-1)2
为奇函数的充要条件是a=-1.

故答案为:-1.

阅读理解

阅读理解。

     The climate of any place is the kind of weather. It usually has

over a long period of time. The houses we live in, the clothes we wear,

and the food we eat depend on the climate of the place where we live.

      Climate is a pattern that is not nearly as simple as we think,

and it is affected by many factors. The distance to the North or

South Pole or to the equator really matters a lot. If you live near

either of the poles, you live in a cold climate, for the place where

  you live does not get as much or as direct sunshine as a place

  farther away from the poles. In places close to the equator, the

climate is very hot, for they are the parts where the sun shines

almost straight down.

     Whether rain or snow falls makes a great difference to the

climate. In hot, dry deserts, little rain falls, but in a hot rainforest,

the amount (数量) of rainfalls is far larger than that in a desert, for

there is a heavy rain almost every day, even several times per day.

Though a rainforest and a desert may be the same distance from the

equator, their climates are rather different from each other.

      How much rain or snow falls is considered by some to be

determined by the winds, the surrounding mountains and the

currents (水流) in nearby seas and so on. In short, it is a very

complex natural phenomenon.

1. This passage mainly talks about   ____.    

A. weather

B. different climates

C. climate and its determining factors

D. the difference between weather and climate

2. From this passage, we know climate and weather are ____ and climate is ____.  

A. almost the same; the general term of weather

B. quite different; the average weather conditions at a particular place over a period of time

C. not the same; included by weather

D. very much alike; bigger and weather is smaller

3. The climates between a tropical(热带的) desert and a tropical rainforest are different in ____   .   

A. the amount of rainfalls

B. the winds and the surrounding mountains

C. the currents in nearby seas

D. how much sunshine the two different places can get

4. From the context, we can guess that the word "complex" means ____   . 

A. simple                        

B. easy to understand

C. rather                          

D. difficult to understand

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