X Y x y X ={ x }, Y ={ y }. , , x Y.
y = f (x). (1.1)
( D(f)), Y . , , , , .
, ,
x = f -1 (y). (1.2)
Y , .
:
1. , ,
y = sin (x);
2. , , .1.1.
3. , , (1,2); (2,5) (4,2). , .
Y, .
f (- x) = f (x). (1.3)
Y. , , y = cos (x).
f (- x) = - f (x). (1.4)
. , , y = sin (x).
, .
(), () , ..
.
.1.1. .
.
0 ,
f (x 0) = 0.
, lg (x) = 0 0 = 1.
, .. , ,
f (x + ) = f (x) = f (x - ). (1.5)
1.
. , , , - . , . , . .
|
|
2. ,
1. ;
2. ;
3.
. :
1. , .. , . :
, , .
2. . , , , .
:
,
- ;
,
;
,
, .
3. .
.
π, , =1.
e- A (A -e, A +e). δ - 0 ( 0 - δ, 0 + δ).
. f (x). A y = f (x) x x 0 ( 0), e > 0 e d(e) > 0 , , ½ x0 - ½<d (.. δ 0), ½ A f (x) ½<e.
. (1.6)
f (x) A 0 , 0, f (x) A.
x 0 f (x) 0, ( ) x 0. a, b, g.
e > 0 e d(e) > 0 , , ½ x0 - ½<d, ½ α() ½<e.
. (1.7)
:
a() = 2x - 6 3,
b() = e-x ¥,
g() = sin x 0 ..
0.
:
()
α() + β () = γ().
α() β () = γ().
α() = γ().
|
|
D, ,
½ f (x)½<
D. .
α() f (x) = γ().
f (x) 0, d() > 0 , , ½ x 0 - ½<d, ½ f (x)½> .
.
, :
y = 1/x 0,
y = l g (x) ¥ + 0 .
. ( ¥) .
:
, , .
.
.
: α() - 0, f (x) = ˗ 0 .
.
, , e > 0 e d(e) > 0 , , ½ x0 - ½<d, ½ α() ½<e. f (x) =
.
, f (x) x x 0.
, .
, 2 - 6 = 3, ˗ . , .