2 + 2 + 2 + 2Dx + 2Ey + F = 0.
( ), , .
1) - .
2) - .
3) - (0;0)
4) - .
5) a2x2 c2y2 = 0 .
6) y2 = 2px .
7) y2 a2 = 0 .
8) y2 + a2 = 0 .
9) y2 = 0 .
10) (x a)2 + (y b)2 = R2 .
.
(x a)2 + (y b)2 = R2 (a; b).
. , :
2x2 + 2y2 8x + 5y 4 = 0.
, .9. :
x2 + y2 4x + 2,5y 2 = 0
x2 4x + 4 4 + y2 + 2,5y + 25/16 25/16 2 = 0
(x 2)2 + (y + 5/4)2 25/16 6 = 0
(x 2)2 + (y + 5/4)2 = 121/16
(2; -5/4); R = 11/4.
,
. (20).
(1) .
9.
, ( 90 ). a , b - .
. . , .
- .
6. ,
(21).
(21) . 10.
. . a , b - , ox , oy .
, , . x . 10 .
- .
7. ,
(22).
(22) . 11. F .
- - .
.
. y = k1x + b1, y = k2x + b2,
|
|
.
, k1 = k2. , k1 = -1/k2.
. + + = 0 1 + 1 + 1 = 0 , 1 = l, 1 = l. 1 = l, .
.
,
.
. , 1(1, 1) = kx + b :
.
. (0, 0), + + =0
.
. 1(1, 1) , . 1:
(1)
x1 1 :
, 0 .
:
A(x x0) + B(y y0) + Ax0 + By0 + C = 0,
, , :
(1), :
. .
. : y = -3x + 7; y = 2x + 1.
k1 = -3; k2 = 2 tgj = ; j = p/4.
. , 3 5 + 7 = 0 10 + 6 3 = 0 .
: k1 = 3/5, k2 = -5/3, k1k2 = -1, , .
. (0; 1), B(6; 5), C(12; -1). , .
: ; 4x = 6y 6;
2x 3y + 3 = 0;
: Ax + By + C = 0 y = kx + b.
k = . y = . .. , : b = 17. : .
: 3x + 2y 34 = 0.
- - . .
- - .
- .
:
; y=f(x) ( f(x)) x, () .
, ( );
;
;
, ;
( ) ( ), ( , , , );
;
;
(, ).
. y x , :
|
|
y = k x,
k - ( ).
, X , k: tan = k (.8). , . .8 k = 1/3, k = 1 k = -3
- , ,
.
, x y. , . , :
v = u 2,
u - , a v - . , u v:
. z , .. z(y), , , , .. (), f(x) = z(y(x)) ( , ) .
, . , z(y).
:
.
, , ( ): z = f1(y1), y1 = f2(y2), , yn-1 = fn(x),
_ .
. ?..
-
_ , 12. ,
. _ -
.
. , , _
-
. , -
.
:
1.
, , , 1
x
, px, npx.
x_.
2.
y = ax.
3.
y = loga x.
4.
, , .
5. .
arcsin x, arccos x, arctg x, arcctg x.
, , , -
, . , y = x2
ex _ -
; y = sin (ax) _ ,
_ .
- . -
y=f(x), N
().
n
, , , - . , :
2, 3, 5, 7, 11, 13, 17, 19, 23, 29,...
.
|
|
, , - .
.
́ ́ ( ) , , , .
: , , ( ); , , ; , , .
. , , , , ; ( ). : , , ( ).
, .. , () . .
, , , ( ). ( ), .
( ) , , .
, ( ).
́ .
- .
- .
. , , .
: , . , .
f(x) , x .
, .
. .
|
|
, , .
, , , .
, , (, ). , .
. , .
, , 0.
, , . , sin, , .
1 :
.
. :
, 7. . :
:
:
: 7/3.
.
, e = 2,718281828 .
, , .
.
, .
..
y=f(x) x→a x→∞, , .. , .
- , ,
- .
- . .
- .
- , ,
- .
- .
- ,
- .
- .
- .
- .
200
, , .
F(x), X, f (x), f (x), x Î X :
F ¢ (x) = f(x). (8.1)
. f (x) f (x); -
∫ f(x) dx..
F(x) - - f (x),
∫ f(x) dx. = F(x) + C, (8.2)
- .
:
45-46 200
, , .
: 0 , 1=
0 1
. [a, b] f(x). [a, b] n a = x < x<...<x = b.
|
|
1 n
(xi-1, xi) xi f(xi)Δ xi, Δxi = xi - xi-1. f(xi)Δ xi , λ = max Δxi→ 0, , f(x) a b :
f(xi)Δ xi. (8.5)
f(x)
[a, b], a b .
:
1);
2);
3) -;
4), (k = const, k∈R);
5);
6);
7) f(ξ)(b-a) (ξ∈a,b]).
- .
f(x) [a, b].
∫f(x) dx = F(x) + C
-, :
f(x) [a, b].
∫f(x) dx = F(x) + C
-, c :
f(x) [a, b].
∫f(x) dx = F(x) + C
-, c :
F(b) - F(a). (8.6)
: , y= f(x), x = a x = b Ox.F(b) - F(a). (8.6)
- .
- . .