:
1. b f(x) = , - , ( - ; + ), , , = , < .
2. f() g(x) , f() + g(x), f(x) g(x), kf(), (g(x) :
3. = f(x) + g(x);
2) = f(x) g(x);
3) kf(x) +k f(x);
4) = , .
4. 0, 0.
5. f() 0 0 , , :
6.
7. = f(u), u = h(x), ' = 'u u'.
1 = k = tg - . v = s'(t); a(t) - v'(t) - . - 0 = f (0)( - 0) - = f(x) 0.
8. , .
9. 䒺, .
10. , .
:
:
1. F(x) f(x) , F(x) = f(x).
2. , 2 2, (2)' = 2.
3. f(x) F(x) + , F(x) - , - .
4. - f(x) , .
5. . .
6. f(x) , .
7. F(x) G(x) - f(x) g(x), F (x) + G(x) f(x) + g(x),
8. F(x) - f(x), a k , b - , :
kF(x) - kf(x);
F(k + b) f(kx+b);
9. ( ) f(x) [; b] F(b) - F(a), F(x) - f(x)
[; b].
10. f(1)+ f(1)+... + f(n).
11. f(1)+ f(1)+... + f(n). f(x) [; ], n , f(x) b
12. - = F(b) - F ) .
13. , .
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:
:
1. : (, ; z) - , z.
2. .
3. (, ; z) - (x1; y1; z1 ) (x2; y2; z2 ),
= , = , Z = =
4. г : + b + z + d = 0.
5. г r:
-
+ + = ;
(; b; )
+ +
6. . . - . () () = ; = ; z = . : = (; ; z).
7. , . .
8. = (, ; z), = .
9. () = () ; ).
10. - . , .
11. , , , D, + + = .
12. г () = () , ; ).
13. - = (, ; z) k : = (k, k; kz).
14. - m, n
m = ( = + ; (m+n) = + ; .
15. :
= .
16. () = (), ; .
:
:
1. , , , .
2. , - , + . - .
3. , - , . - .
4. 1 n- !.
5. k- n- k . .
- k (n k)
= n(n-1) (n-k+1).
6. k , n.
7. . .
8.ʳ n n!: = n!.
k - k- n- . ʳ k :
=
9. - , , , .
10. - .
11. - , .
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12. .
13. 䳺 볭 . Q ().
14. 䳿 () 䳿 - , :
() =
.
15. 䳿:
1) , () = 0;
2) - , () = 1;
3) X - , 0 < () < 1;
4) 2, 3, ..., - 䳿, , P(E1) + (2) + (3) +... + () = 1.
16. , 䳿 . 䳿 ( , ). 䳿 . .