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- , [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 .





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