2.7.1 . .
:
1.
2. .
, . , .
, .
, , .
, y , .
() , Y .
:
1. . .
2. , , .
3. , , .
4. , .
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1. . , , , . .
. , , .
, .
2.
. () , () (. ). , , , . .
3. . , , .
4. . , .
, , : , .
, , : .
, Y. , . , Y , . ( !). : ,
, . ( ), 1- 3- (, ) (. .)..
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u, U Y, u, , , U. ( , ).
, , .. , .
:
1. : ( , ).
2. : .
3. : .
4. : , , , .
5. : , , , .
. :
1. , O; , .
2. , Oy; , .
3. :
- m Oy, ;
- m Oy, ;
- m Oy Ox, ;
- m Oy Ox, .
4. :
- k Ox, ;
- k Ox, ;
- k Ox Oy, ;
- k Ox Oy, .
.
n , , : . , .
, n - .
: 2, 4, 6, , 2 n, ( ); 1, 0, 1, 0, ( 0 1).
, , ,
(7.1)
. , , , .
: n , , e, .
y = f(x) , , e > 0 S > 0, | | > S
| f(x) A | < e (7.2)
f(x) = A, f(x) A ¥.
.
f(x) 0, e > 0 d = d(e) > 0, x ¹ x 0, | x0 | < d | f(x) A | < e.
: , 0, f(x) .
|
|
1. 0, , 0, 0. 0 0, 0.
2. 0 , 0, f(x) , :
f(x) = A
, 0, > 0 , .:
f(x) = A
f(x) = f(x), f(x) = A.
a(x) , :
a (x) = 0
:
: f(x) = A, f(x) f(x) = A + a(x), a(x) 0 (¥).
: f(x) a (x) 0 (¥), 0 (¥), ..
f(x) = A
:
1. .
2. .
3. , , .
. 3 a (x) b (x) - . , ¹ 0 ¥. a (x) b (x). : a (x) = o(b (x)) 0 (¥), .. a (x) b (x). a (x) b (x) ( a (x) b (x) b (x) = O(a (x))). a (x) b (x). a (x) b (x) a (x) b (x).
f(x) 0, M > 0 d > 0 (d (M)), x ¹ x 0, | x0 | < d : .
:
1. , , .
2. .
3. , 0, .
:
: a (x) 0 (¥), 0 (¥). , a (x) 0 (¥), 0 (¥).