.


:




:

































 

 

 

 





f (x) g (x) a . , , , . f (x) A, = ¥, + g (x)) = [ A + ( ¥)] = ¥, g (x)) = [ A ( ¥)] = K ¥,

= f (x) A, = ¥ = 0,

:

,

g (x)) = [¥ ¥], =[0¥], , .

, f (x) g (x). ,

1) ;

2) [¥ ¥] .

, , [0¥], , .

e, : = . , [0¥], ,

1) = 0, = ¥ 2) = ¥, = 0.

, = 0, = 1, = +¥, = +¥, = ¥, = 0.

, , : [1¥], [00], [¥0].

, .

 

:

, , .

= e [1¥] : , . .

.. ( 4, 4).

 

4.

. f (x), f 1(x), g (x), g 1(x) x a, f (x) ~ f 1(x), g (x) ~ g 1(x). , , =

.

. ,

= =

= 1 1 = . .

, , , . , a(x) x a, , x a(x), ,

 

. . , a(x) x a,

sin a(x) ~ a(x), tg a(x) ~ a(x), arcsin a(x) ~ a(x), arctg a(x) ~ a(x),

ln (1+a(x)) ~ a(x), e a(x) 1 ~ a(x).

.

1.

.

x 0: sin 5 x ~ 5 x tg 3 x ~ 3 x .

2.

.

x 3: ln (1+ x 3) ~ x 3 tg 2(x 3) ~ 2(x 3) .

 





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