Proc37. Power1(A, B) , -
A B A B= exp(B ln(A)) ( A B ).
A -
0. A P, B P, C P,
P, A, B, C.
Proc38. Power2(A, N) , -
A N(A , N )
:
A 0= 1;
A N= A A ... A (N ), N > 0;
A N = 1/(A A ... A) (| N | ), N < 0.
A K, A L, A M, A, K, L, M.
Proc39. Power1 Power2 ( Proc37 Proc38), -
Power3(A, B) -
, A B : B
, Power2(A, Round(B)); -
Power1(A, B).
A P, B P, C P, P, A, B, C.
Proc40◦. Exp1(x, ε) ( x, ε
, ε > 0),
exp(x):
exp(x) = 1 + x + x 2/(2!) + x 3/(3!) +... + x n/(n!) +...
(n! = 12... n). , ε.
Exp1 x
ε.
Proc41. Sin1(x, ε) ( x, ε
, ε > 0), sin(x):
sin(x) = x x 3/(3!) + x 5 /(5!) −... + (−1)n x 2n+1/((2 n +1)!) +....
, ε. -
Sin1 x
ε.
Proc42. Cos1(x, ε) ( x, ε
, ε > 0), cos(x):
cos(x) = 1 x2 /(2!) + x4 /(4!) −... + (−1)n x2n /((2 n)!) +....
, ε.
Cos1 x
ε.
Proc43. Ln1(x,ε) ( x,ε
, | x | < 1, ε > 0),
ln(1 + x):
ln(1 + x) = x x2 /2 + x 3/3 −... + (−1)n x n+1/(n +1) +....
, ε.
Ln1 ln(1 + x) x
ε.
Proc44. Arctg1(x, ε) ( x, ε
, | x | < 1, ε > 0),
arctg(x):
arctg(x) = x − x 3/3 + x 5/5 −... + (−1)n x2n +1/(2 n +1) +....
|
|
|
, ε.
Arctg1 arctg(x) x
ε.
Proc45. Power4(x, a, ε) ( x,
a, ε , | x | < 1; a, ε > 0),
(1 + x)a:
(1 + x)2 = 1 + a x + a (a −1) x2 /(2!) +... + a (a −1)...(a − n +1) xn /(n!) +....
, ε.
Power4 (1 + x)a x a
ε.
Proc46. NOD2(A, B) ,
() A B,
:
(A, B) = (B, A mod B), B 6= 0;
(A, 0) = A.
(A, B),
(A, C), (A, D), A, B, C, D.
Proc47. NOD2 Proc46,
Frac1(a, b, p, q), a / b p / q (
, a b , p q ).
p / q (. . q > 0).
Frac1 , a / b + c / d, a / b + e / f,
a / b + g / h ( a, b, c, d, e, f, g, h ).
Proc48. , -
44
. . . Programming Taskbook 4.6
A B A (B /(A, B)), (A, B)
A B, NOD2 Proc46,
NOK2(A, B) , -
A B. NOK2
(A, B), (A, C), (A, D), A, B, C, D.
Proc49. (A, B, C) = ((A, B), C) -
NOD2 Proc46, NOD3(A, B, C)
, -
A, B, C.
(A, B, C), (A, C, D) (B, C, D), A,
B, C, D.
Proc50. TimeToHMS(T, H, M, S), -
T ( ) H, M
S (T , H, M S ).
, ,
T 1, T 2,..., T 5.
Proc51. IncTime(H, M, S, T), T -
, H, M S (H, M S
, T ;
). ( H, M, S)
T. IncTime,
T H, M, S.
Proc52. IsLeapYear(Y) , -
TRUE, Y ( ) ,
FALSE . IsLeapYear
Y. , -
4, , 100
|
|
|
400.
Proc53. IsLeapYear Proc52,
MonthDays(M, Y) ,
M - Y (1 ≤ M ≤ 12, Y > 0 ).
MonthDays Y M 1, M 2, M 3.
Proc54. MonthDays Proc53,
PrevDate(D, M, Y), , -
D, M Y,
( D, M, Y
). PrevDate
.
Proc55. MonthDays Proc53,
NextDate(D, M, Y), , -
D, M Y,
( D, M, Y
). NextDate
.
Proc56. Leng(x A, y A, x B, y B) , -
AB :
| AB |= 
(x A, y A, x B, y B ).
AB, AC, AD, A, B, C, D.
Proc57. Leng Proc56,
Perim(x A, y A, x B, y B, x C, y C) ,
ABC (x A, y A, x B, y B, x C, y C
).
ABC, ABD, ACD, A, B, C, D.
Proc58. Leng Perim Proc56 Proc57,
Area(x A, y A, x B, y B, x C, y C) ,
ABC
S ABC= 
p . -
ABC, ABD, ACD, A, B, C, D.
Proc59. Leng Area Proc56 Proc58,
Dist(x P, y P, x A, y A, x B, y B) ,
D (P, AB) P AB
D (P, AB) = 2 S P AB/| AB |,
S P AB PAB.
P AB, AC, BC,
P, A, B, C.
Proc60. Dist Proc59,
Heights(x A, y A, x B, y B, x C, y C, h A, h B, h C), h A, h B, h C -
ABC ( ),
A, B, C ( ). -
ABC, ABD, ACD,
46
. . . Programming Taskbook 4.6
A, B, C, D.
-
, -
.
:
,
.
, -
( , N
).
Minmax1◦. N N .
.
Minmax2. N N , -
(a, b). -
.
|
|
|
Minmax3. N N , -
(a, b).
.
Minmax4◦. N N . -
.
Minmax5. N N (m, v) -
m v , . -
, ,
. P
P = m / v.
Minmax6◦. N N .
.
Minmax7. N N .
.
Minmax8. N N . -
.
Minmax9. N N . -
.
Minmax10. N N . -
( )
.
Minmax11. N N .
( )
.
Minmax12◦. N N .
.
, 0.
Minmax13. N N . -
.
, 0.
Minmax14. B (> 0) .
, B, .
, B, , 0
Minmax15. B, C (0 < B < C) .
, (B, C),
. ,
0.
Minmax16. N N .
, .
Minmax17. N N .
, .
Minmax18. N N .
, -
. ,
0.
Minmax19◦. N N .
.
Minmax20. N N . -
48
. . . Programming Taskbook 4.6
( )
.
Minmax21. N (> 2) N
, N . -
.
.
Minmax22◦. N (> 2) N . -
|
|
|
.
Minmax23. N (> 3) N . -
.
Minmax24. N (> 1) N .
.
Minmax25. N (> 1) N .
,
, , .
Minmax26. N N . -
, .
, 0.
Minmax27. N N ,
. ,
,
. ,
.
Minmax28. N N , -
. ,
, -
. ,
. ,
0.
Minmax29. N N . -
.
Minmax30. N N .
.
N , -
( N), -
. ,
, ,
2 10. 1.
, () ,
, ,
() ,
.
