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ENG
 

            

(, , )  

(, , )

,

:

: (, , )

: 1

( )

..

: ..

2002


2



堠 3

2. 4

2.1 5

2.2 6

3. 8

3.1 ࠠ 8

3.2 ࠠ 9

3.3 ࠠ 10

ࠠ 12

















































3

 


, , , , , , .

. (, , . , .).






































4


2.


f (x) x > (

x < ). k l, f(x) - kx - l = 0 + ¥ ( - ¥),

y = kx + l

f (x) x + ¥ ( - ¥).

, + ¥

( - ¥) , .

x- 3x - 2

, , y = x +1

,

2 2

y = x - 4 + x + 1 ꠠ x + 1 = 0 ¥, y = x-4

+ ¥,

- ¥.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5

 

2.1

 

. = (x, f (x)) f, - , ,

q - , q ¹,

MP , , Q (.1).

(.1)


= f (x), QM = kx + l, MQ = MM - QM = f (x) (kx +l),

MP = MQ cos q. , MP MQ cos q, MQ 0 MP 0 + ¥ ( - ¥) , lim MQ = 0,

lim MP = 0, . + ¥

+ ¥

, , , , , = (x, f (x)) , , ( + ¥ , , - ¥).


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


6

 

2.2

 

, k l y = kx + l.

+ ¥ ( - ¥ ). f y = kx + l + ¥. , ,

f (x) = kx + l + 0

f (x) = kx + l + 0 + ¥.

lim = k.

+ ¥

k, f (x) = kx + l + 0 l

l = lim (f (x) kx).

+ ¥

: k l, l = lim (f (x) kx), y = kx + l

+ ¥

f (x). , l = lim (f (x) kx)

+ ¥

lim [f (x) - (kx + l)] = 0,

+ ¥


y = kx + l , , f (x) = kx + l + 0. , lim = k. l = lim (f (x) kx)

+ ¥ + ¥

y = kx + l . , ,



f f (x) = kx + l + 0, k l lim = k. l = lim (f (x) kx)

+ ¥ + ¥

, y = kx + l, .

f (x) = ,

:


7



, ,

y = x 4, + ¥, - ¥.

y = kx + l , Oy. , Oy.

































8


3.

3.1

 

$ lim f (x) = b. , f (x) y = b. ( x +¥) (.2)



(.2)



, (.3)



 

(.3)

 

 

 

 

 

 

 

 

 

 

 

 


9

 

3.2


(.4)



x a 0 lim f (x) = ¥. , x = a

¥

f (x). f (x) x (.4), , , , , f (x) + ¥ - ¥.

, f (x)

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


10


3.3

 

(.5)


y = ax + b. d = ax + b f (x). , d = ax + b f (x) 0 ¥

lim [f (x) (ax + b)] = 0.

x ¥

, ࠠ

,

, b


.


x +¥ y=x.

11


, x - ¥ y = - x.

(.6)

(.6)





























12

 

 

1.     .. , , 1991.

2.     .. .1, 1981

3.    

 



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