1.
2.
3.
4. ѳ
5. -
6.
f(x) [a;b]. . f(x) F(x), -
, ` . , , , . . , : f(x) [a;b], - , [a;b] , =f(x) =, =b. , [a;b], . =S , , .
f(x) [a;b], - [a;b] .
, [x ;x +h] [x ;x +h] , [x ;x +h],
.
, [x ;x +h] , .
` [a;b] n h=
[ ] , .
. [ ] (= ) , , , . ³,
S , =S =h .
.
, [x ;x +h] [x ;x +h] , [x ;x +h],
.
, [x ;x +h] , .
` [a;b] n h=
[ ] , .
. , [ ] , i=( ), : S , =S =h .
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, [x ;x +h] [x ;x +h] , [x ;x +h],
.
, [x ;x +h] , .
` [a;b] n h=
[ ] , .
. , , , , . S , =S =h .
, [x ;x +h] =f(x) , , =f(x). f(x ) f(x +h) h, , , , ` [a;b] n , .
, ` . , n , h, , i=( ) . , =S =h , .
ѳ.
ѳ , [x ;x +2h] =f(x) , ( ;f(x )), ( +h;f(x +h)), C( +2h;f(x +2h)), =f(x). , [x ;x +2h] . , , `. : , =x +h, =x +2h. .
. =x +h, (-x )*(- )=(-x )*((-x )-h)=(-x ) -(-x )*h i . S
. - , - , S ) (1), .
[a;b] n , n- , n=2m, .
- . .` , . (1).
, ,
(2)
(2) ѳ. (2) . >0 . ` . S (2) n=2,4,8,...,2 ,..., . ϳ (n>2) : . , . = - , >0. .
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-.
: , y=f(x), x=a, x=b [a;b]. , . S , . S - . N , S. N - , . . .
1: max y=f(x) [a;b] :
1) 1) b-a,
2) 2) max(f(x)).
2: , .
3: . .
.
, . [a;b] , y=f(x). [a;b],
. , [a;b] f( ). , . , . ³ ( <0, ). Q, Q =f( ). ` Q , Q, , b. , b = , . ij, .
: f(x)>0. - [a;b] y=f(x). , f(x) [a;b]. 2 . , , , `. , b M, ` b M= .
.