Профессиональные математические пакеты

,

К:7, Л:10, К+Л,

«VТОа»,

.

ЬЮЦ, pЫШН.

1

100.

1

50.

6.2.3

MКбТmК

MКбТЦК.

.

1.

,

:

,

,

,

,

;

,

,

.

2.

г:

z: makelist(n*(n+1)/2,n,1,10).

3.

:

z: makelist(random(30),n,1,10).

4.

:

5.

.

,

;

;

,

5

7;

;

;

;

;

92

6.

3

: a

b,

,

a < z[i] < b;

: a

b,

,

ab < z[i];

: a

b,

,

b − a < z[i]2;

,

;

,

;

93

. 6

:

1)

;

2)

,

;

3)

;

4)

.

а

а

а

ЫКЭЬТЦp (

. . 3.1).

,

:

ЭЫТРЬТЦp ( . . 3.1).

,

:

1

9 tan6 x + 29 tan4 x + 39 tan2 x + 8 sin6 x + (24 cos2 x + 7) sin4 x+

+ (24 cos4 x + 14 cos2 x + 6) sin2 x + 8 cos6 x + 7 cos4 x + 6 cos2 x + 23

2

9 tan6 x + 36 tan4 x + 51 tan2 x + 8 sin6 x + (24 cos2 x + 5) + sin4 x+

+ (24 cos4 x + 10 cos2 x + 2) sin2 x + 8 cos6 x + 5 cos4 x + 2 cos2 x + 34

6

3 tan6 x + 12 tan4 x + 17 tan2 x + 2 sin6 x + (6 cos2 x + 9) + sin4 x+

+ (6 cos4 x + 18 cos2 x + 1) sin2 x + 2 cos6 x + 9 cos4 x + cos2 x + 18

7

4 tan6 x + 17 tan4 x + 27 tan2 x + sin6 x + (3 cos2 x + 6) + sin4 x+

+ (3 cos4 x + 12 cos2 x + 8) sin2 x + cos6 x + 6 cos4 x + 8 cos2 x + 25

8

6 tan6 x + 24 tan4 x + 37 tan2 x + 9 sin6 x + (27 cos2 x + 1) + sin4 x+

+ (27 cos4 x + 2 cos2 x + 6) sin2 x + 9 cos6 x + cos4 x + 6 cos2 x + 28

9

9 tan6 x + 30 tan4 x + 34 tan2 x + 9 sin6 x + (27 cos2 x + 4) + sin4 x+

+ (27 cos4 x + 8 cos2 x + 1) sin2 x + 9 cos6 x + 4 cos4 x + cos2 x + 25

10

7 tan6 x + 24 tan4 x + 29 tan2 x + sin6 x + (3 cos2 x + 7) + sin4 x+

+ (3 cos4 x + 14 cos2 x + 8) sin2 x + cos6 x + 7 cos4 x + 8 cos2 x + 27

а

а

а

ЫКНМКЧ (

. . 3.1).

,

:

log(

x(3x3

+6x2+x+3)

) − log(

x(2x2+4x+5)

)

1

e

e

x5

x5

log(

x(8x3

+7x2+8x+4)

) − log(

x(4x2+4x+1)

)

2

e

e

x4

x

log(

x(9x3

+7x2+5x+3)

) − log(

e

x(x2+4x+8)

)

3

e

x

x

95

log(

x(8x3+7x2+5x+6)

) − log(

x(4x2+7x+7)

)

4

e

e

x

x3

log(

x(3x3+x2+8x+4)

) − log(

x(7x2+x+8)

)

5

e

e

x3

x2

log(

x(7x3

+2x2+x+4)

) − log(

x(8x2+6x+4)

)

6

e

e

x5

x

7

log(ex(5x3+3x2+x+1)x4) − log(ex(4x2+7x+1)x3)

log(

x(3x3

+3x2+8x+3)

) − log(

e

x(x2+9x+3)

)

8

e

x2

x2

log(

x(5x3+3x2+9x+1)

) − log(

x(9x2+6x+9)

)

9

e

e

x5

x

log(

x(x3+8x2+9x+3)

) − log(

x(7x2+3x+7)

)

10

e

e

x5

x4

6.2.5

Р

а

ЬШХЯО ( . 3.2).

:

9z + 9y + x + 2 = 0

1

6z + 5y + 9x + 6 = 0

5z + 8y + 2x + 8 = 0

3z + 2y + 7x + 9 = 0

2

2z + 7y + 2x + 5 = 0

9z + 7y + 2x + 1 = 0

8z + 8y + 2x + 7 = 0

3

8z + 6y + 7x + 7 = 0

8z + 4y + 7x + 6 = 0

96

2z + y + 6x + 5 = 0

4

9z + 2y + 9x + 2 = 0

4z + 2y + 2x + 5 = 0

7z + 2y + 3x + 8 = 0

5

6z + 5y + 5x + 8 = 0

8z + 3y + 7x + 9 = 0

z + 5y + 9x + 2 = 0

6

7z + 8y + 4x + 3 = 0

6z + 2y + x + 9 = 0

6z + 4y + 9x + 6 = 0

7

8z + 9y + 5x + 5 = 0

6z + 3y + 7x + 4 = 0

5z + 2y + 3x + 9 = 0

8

2z + 6y + 8x + 8 = 0

z + 3y + 7x + 9 = 0

8z + 3y + 9x + 6 = 0

9

5z + 4y + 2x + 5 = 0

2z + 2y + 4x + 7 = 0

z + 9y + 4x + 4 = 0

10

2z + 6y + 7x + 3 = 0

z + y + 4x + 9 = 0

Р

а

а

.

1.

:

d2

d

y (x) + p

y (x) − qy (x) = 0.

dx2

dx

p q

.

p

9

9

1

10

7

2

10

10

3

q

1

9

10

3

5

7

9

8

9

.

.

d2

d

y +

y + 2y = xe−x ,

dx2

dx

98

7

–

,

.

.

MКбТЦК

,

(

. . 6.2).

.

:

V = (N K) div 100,

V –

, n –

, div –

(

V = 0

), K –

.

7.1

1.

.

2.

.

3.

.

7.2

:

1.

( .

).

2.

3.

,

:

;

MКбТЦК,

;

,

MКбТЦК.

.

».

log(

e

x(7x3

+6x2+9x+4)

) − log(

e

x(9x2+9x+8)

).

x3

x

-loР(\%e^(б*(9*б^2+9*б+8))/б));

−2 log (x) + 7x4 − 3x3 − 4x

(%Ш1)

4.

:

,

.

T

5 × 5.

(%Т1)arraв(T,5,5);

T

(%Ш1)

.

done

(%Ш2)

.

(%Т3)Пor Т:1 tСru 5 do

(s:makelТst(T[Т,j],j,1,5),prТnt(s));

[84, 70, 66, 87, 38]

[74, 78, 18, 61, 71]

[80, 15, 70, 97, 78]

[94, 25, 92, 47, 8]

[18, 50, 63, 20, 7]

done

(%Ш3)

.

(%Т4)TeskA(T,n):=block([s:0,Т,j],

Пor Т:1 tСru n do

Пor j:1 tСru n do

(