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0x .
. 1f (x)x 1
=
( ) ( )A {1} ,1 1,= = + , f 0x 1= x 1 f(x) , , + . f + x 1
1=+
x 1lim
. f:A IR , ( ) ( )0 0,x x , . :
0 0 0x x x x x xlim f (x) lim f (x) lim f (x) +
= + = = +
0 0 0x x x x x xlim f (x) lim f (x) lim f (x) +
= = =
:
0x xlim f (x) = + f(x)>0 0x
0x x
lim f (x) = f(x)
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0x x
lim f (x) = + 0x x1lim
f(x)=0
00
x xx x
0
A lim f(x) 0 1 : limf(x) f(x) 0 x
= = +>
00
x x
x x0
A lim f(x) 0 1 : limf(x) f(x) 0 x
= = <
0x x
lim f (x) = + 0x x1lim 0
f (x)=
:
0x xlim f (x) = + 0x xlim | f (x) | = +
:
0x xlim f (x) = + 0
x xlim f(x)
= + * : f(x) g(x) 0x
0x xlim f (x) = + 0x xlim g(x) = +
f (x) g(x) 0x 0x x
lim g(x) = 0x xlim f (x) =
. ( * )
) 2x 01limx
= + 2x 01lim
x= + ( )0 2x x 0
1limx x
= +
) x 0
1limx+= + 2 1x 0
1limx+ +
= + ( )0 2x x 01lim
x x+= +
: , +
) x 0
1limx= 2 1x 0
1limx +
= ( )0 2x x 01lim
x x
=
: ,
. : 1 ( )
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x0 f : R R + + g : + + +
gf + : + + ; ;
2 ( )
x 0
f : >0 0
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