- , [a,b], y=f(x), f(x) , 2 x=a,x=b. - , S , ox. S . ., . +, - -.
S, y=f1(x), y=f2(x), x=a, x=b, f1(x)≤ f2(x) a≤x≤:
S=
, Ox , y=f(x)≥0 x=a, x=b (a<b), y=0:
=
, Oy , x=g(y)≥0 y=a, y=b (a<b), x=0: V =
.
1)
f(x) [a;+∞) [a;R] ,
∃
R→+∞ , - f(x) [a;+∞).
(1)- 1
, , , lim , ,
- ,
2)
-
f(x) . [a,b)
(∙)x=b-. (∙), - (∙), [a,b-𝜇], [a,b).
[a,b-𝜇] - ,
∃ , ∀𝜇>0, b-𝜇>a
𝜇→0 lim, 2 .
, (), , .
.
1) .
a)f(x)g(x)- . [a,+∞)
0≤ f(x)≤ g(x)
2) f(x)g(x) - x→+∞,
3) .
x→+∞ . - f(x) . 𝛾(𝛾>0), 𝛾>1 𝛾≤1.
2. - x≥a . ,
. . .
- -, - -- .
|
|
1) , - 1
2) , - - 2 .
- -.
n- , -
F(x, y(x),y(x), y''(x),, y(n)(x))=0
- y=𝜑(x), .
.
- . - - -.
1 - - F(x, y, y)=0, x- , y- -, y'- .
y', y'= dy/dx =f(x,y)- - 1 , .
P(x,y)dx+Q(x,y)dy=0.
( 1 )
- f(x,y) f'y(x,y) G oxy, (x0, y0) G, - y'= f(x,y), y=y0, x=x0
, (y0, x0) G .