→ | "", "" |
↔ | |
: | ", " |
∀x: |x|<2 → x2 < 4 : x , |x|<2, x2 < 4.
.
, .
- ∀- , " ", " ".
- ∃- , "", "". ∃!, .
(=), .
, ={1,2,3,4}, B={3,1,4,2} =.
() ∪ , .
, ={1,2,4}, B={3,4,5,6}, ∪ B = {1,2,3,4,5,6}
() ∩ , , .
, ={1,2,4}, B={3,4,5,2}, ∩ = {2,4}
, , .
, ={1,2,3,4}, B={3,4,5}, = {1,2}
Δ , , Δ = () ∪ ().
, ={1,2,3,4}, B={3,4,5,6}, Δ = {1,2} ∪ {5,6} = {1,2,5,6}
A ∪ B = B ∪ A
A ∩ B = B ∩ A
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
, - , .
, , .
1
.
2.
.
, , , , x , y .
.
1. .
- .
, , , , . .
- . x = 1 , x = 3 . .
|
|
X .
:
, . , y, . , , .
. , x , , ( ), . , = 3, :
. , = 3 -4/3.
, - , t. ,
t = 2, x = 2, y = 4. , = 2 4.
2. .
(x,y). . :
3. .
. .
1, ; 0, .
4. .
, . , , Y.
:
. , , .
3.
f (x) g (x), ,
, x = a. x = a , / , .
: .
f (x) g (x)
a , + ∞ − ∞. , a . x .
1 |
. . x = 1, , x = 1. , |
.
2 | |||||||||||||||||||||||||||||||||||||||
.
.
y = −2. .
( : ax 2 + bx + c = a (x − x 1)(x − x 2), x 1 x 2 - .) ,
,
|
4. 5.
.
, x y, . . , (x; y), t (a; b). , 3.
.
, , .
x. , n- .
.
, .
. , x.
: . , , .
.
, .
.
.
, . :
: .
, x t, x t ( ), , .
|
|
, :
.
,
.
,
, .
, : .
, :
,
:
,
.
6.
y (x) . ,
y (x) .
y' (x) :
- x, ,
y - x ;
- y' (x).
1 |
y (x), . . x: |
2 |
y (x), y = 1. . x ( ): y = 1, |
.
(1) x = −1 y = 1.
, y' = 0 y = 1.
3
x 2 + y 2 = r 2 r.
y' (x).
.
x :
. , , y (x) . ,
4 |
x 4 + y 4 = 2 (1;1). . x: . (1;1) , y' (1) = −1. , |
7.