МЕТОДИЧЕСКОЕ ОБЕСПЕЧЕНИЕ 1 КУРС 2 СЕМЕСТР / математика_задание_1 курс_Весна_2013

Буква

Номер варианта

А

1

Б

2

В

3

Г

4

Д

5

Е, Ё

6

Ж

7

З

8

И, Й

9

К

10

Л

11

М

12

Н

13

О

14

П

15

Р

16

С

17

Т

18

У

19

Ф

20

Х

21

Ц, Ю

22

Ч

23

Ш,Щ

24

Э, Я

25

Вариант № 1.

1:

z = 2x3y 4xy3:

:

z

p

2:

z = x2 + y2 + 3; x = ln t; y = p3 t:

yp

2

y2

x

y:

3

=

x

+ 14

3x + y xy;

4:

z =

D : y = x; y = 4; x = 0:

Вариант № 2.

1:

z = arctg x + p

y:

z = x2e y

x = cos(u v); y = sin

u

2:

;

:

v

3:

z = x3 + 8y3 6xy + 5:

4:

z = xy x 2y; D : x = 3; y = x; y = 0:

Вариант № 3.

1:

z = x2y sin x 3y:

2:

z = ln ex

+ e y

; x = t3; y = t2:

3

:

z

= 1

xy

2y2:

+ 15x

2x2

4:

z = x2 + 2xy 4x + 8y;

D

: x = 0; y = 0; x = 1; y = 2:

Вариант № 4.

1:

z = arcsin xy 3xy2:

y2

p

3:

z = 1 + 6x x2

xy

:

2:

z = sin x cos y; x = ln

u + v2

; y =

v

u2:

4:

z = 5x2 3xy + y2;

D

: x = 0; x = 1; y = 0; y = 1:

Вариант № 5.

1:

z = 5xy4 + 2x2y7:

2:

z =

x

; x = eu v; y = sin(u + v):

x y

3:

z = 2x3 + 2y3 6xy + 5:

4:

z = x2 + 2xy y2 4x;

D

: x y + 1 = 0; x = 3; y = 0:

Вариант № 6.

1:

cos

x2 y2

+ x3:

y

v

2:

z = x ;

u

;

y = ln(v u):

x = e

3:

z = 3x3 + 3y3 9xy + 10:

4:

z = x2 + y2 2x 2y + 8;

D

: x + y = 1; y = 0; x = 0:

Вариант № 7.

:

z

= ln2

3x2

2y2

:

1

y

;

y = cos uv:

2:

z = x e

x = sin(u v);

3:

z = x2 + xy + y2 + x y + 1:

4:

z = 2x3 xy2 + y2;

D

: x = 0; x = 1; y = 0; y = 6:

Вариант № 8.

1:

z = 5xy2 3x3y4:

p

3:

z = 4(x y) x2

y2

:

1

; y =

v2:

2:

z = x sin xy;

x = ln

u2

1

z = 3x + 6y x2 xy y2;

: x = 0; x = 1; y = 0; y = 1:

4:

D

Вариант № 9.

1:

z = arcsin(x + y):

2:

z = xy;

x = ln(u v);

u

y = ev :

3:

z = 6(x y) 3x2 3y2:

4:

z = x2 2y2 + 4xy 6x 1;

D

: x = 0; y = 0; x + y = 3:

Вариант № 10.

1:

z = arctg(2x y):

p

2

=

2

y

2

:

z

arcsin

x

;

y =

x2 + 1:

3:

z = x + xy + y 6x 9y:

4:

z = x2 + 2xy 10;

D

: y = 0; y = x2 4:

Вариант № 11.

1:

z = 7x3y p

xy:

u

2:

z = x2 ln y; x =

; y = 3u 2v:

v

3:

z = (x 2)2 + 2y2 10:

4:

z = xy 2x y; D : x = 0; x = 3; y = 0; y = 4:

Вариант № 12.

1: z = py

x2x+ y

+ 2 3

+ 1

2

2

xy

:

2:

z = e ; x = u ;

y = u sin v:

3: z = (x 5)2 + y2 + 1:

4:

z = 0; 5x2 xy;

D

: y = 8; y = 2x2:

Вариант № 13.

1: z = ex+y 4:

2x

y = cos2 t:

2:

z = arccos

;

x = sin t;

y

3:

z = x3 + y3 3xy:

4: z = 3x2 + 3y2 2x 2y + 2;

D

: x = 0; y = 0; x + y = 1:

Вариант № 14.

1:

z = cos(3x + y) x2:

2:

z = arcsin

x

;

x = sin t;

y = cos2 t:

2y

3: z = 2xy 2x2 4y2:

4: z = 2x2 + 3y2 + 1; D : y = r

; y = 0:

9 4x2

Вариант № 15.

9

x + y

1:

z = tg

:

x y

2:

z = ey 2x 1;

x = cos t;

y = sin t:

3:

z = xp

x2 y + 6x + 3:

y

z = x2 2xy y2 + 4x + 1;

4:

D : x = 3; y = 0; x + y = 1:

Вариант № 16.

1:

z = ctg

y

:

x

2:

z = ln e x + ey

; x = t2; y = t3:

3:

z = 2

5

x2

3

+ 2

xy

y2

:

z = 3x2 + 3y2 x y + 1;

: x = 5; y = 0; x y = 1:

4:

D

Вариант № 17.

1:

z = xy4 3x2y + 1:

2:

z = x2e y;

x = sin t;

y = sin2 t:

3:

z = xy (12 x y) :

4:

z = 2x2 + 2xy 0; 5y2 4x;

D

: y = 2x; y = 2; x = 0:

Вариант № 18.

:

z

ln

x + xy

y2

:

1

=

y

2x

;

3

:

2:

z = e

x = sin t;

y = t

3:

z = xy x2 y2 + 9:

5

4:

z = x2 2xy +

y2 2x; D : x = 0; x = 2; y = 0; y = 2:

2

Вариант № 19.

1:

z = 2x2y2 + x3 y3:

2:

z = xy; x = et; y = ln t:

3:

z = 2xy 3x2 2y2 + 10:

4:

z = xy 3x 2y; D : x = 0; x = 4; y = 0; y = 4:

Вариант № 20.

z = p

:

1:

3xx2 2yy2 + 5

2

3

2:

z = ln (e + e ) ; x = t ; y = t :

3:

z = x3 + 8y3 6xy + 1:

4:

z = x2 + xy 2;

D

: y = 4x2 4; y = 0:

Вариант № 21.

1:

z = arcsin

x + y

:

x

2:

z = x2ey;

x = cos t;

y = sin t:

3:

z = yp

y2 x + 6y:

x

z = x2y(4 x y);

: x = 0; y = 0; y = 6 x:

4:

D

Вариант № 22.

1:

z = arctg(x y):

2:

z = ey 2x+2;

x = sin t;

y = cos t:

3:

z = xy(6 x y):

4:

z = x3 + y3 3xy;

D : x = 0; x = 2; y = 1; y = 4:

Вариант № 23.

p

2

1:

y2 + x :

z = 3x2

t

x

; x = ln(t 1);

2:

z = y

y = e :

3:

z = x2 + y2 xy + x + y:

4:

z = 4(x y) x2 y2;

D

: x + 2y = 4; x 2y = 4; x = 0:

Вариант № 24.

1:

z = y2 + 3xy x4:

2:

z = ln e2x + e y ; x = t4; y = t3:

3

:

z

= 2

xy2

+

x3

5x2 + y2:

z = 6xy 9x2 9y2 + 4x + 4y;

: x = 0; y = 0; x = 1; y = 2:

4:

D

Вариант № 25.

:

z

arcsin

x2

+ y3

:

1

=

2

2

t

; y = cos t:

2:

z = x

+ (x + y) ;

x = e

3:

z = 3x2 x3 + 3y2 + 4y:

4:

z = x4 y4;

D

: x2 + y2 = 1:

1:

dx

f(x; y) dy:

1 p

1 x2

2:

ZZ 12x2y2 + 16x3y3 dxdy; D : x = 1; y = x2; y = p

x:

D

3: x = 4y y2; x + y = 6:

p

p