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) .