математика_2семестр

x3y2

1

U(x; y; z) =

; M0

1; 2; p

:

z

6

~

(

) =

2

(

)

+

2

2

+

2

+ 2

~

~

~

x; y; z

x

z

~{

~|

x

k:

F

y

z

xyz

xyz

F (x; y; z) = (2x + 3yz)~{ + (2y + 3xz)~| + (2z + 3xy) k:

~

5)~|; L : y = x

2

+ 3x

2;

y = 5x + 1:

F (x; y) = (x + 4y)~{ + (2x

1

1

1

U(x; y; z) =

; M0

2;

; p

:

x2yz

3

6

~

2

2

2

~

~

F (x; y; z) = zx + 2y ~{ + zy + 2x ~| z (x + y) k:

~

F (x; y; z) = yz~{ + xz~| + xyk:

~

2

+ 4x 3; y = x + 4:

F (x; y) = (x 4y)~{ + (5x 2)~|; L : y = 2x

~

(

) =

2

22

2

+

2

22

2

2

(

+2

~

~

z

x

)~

F

x; y; z

zx

y

~{

zy

x

~|

y

k:

~

(

) =

2

xy

+

z

~{

+

2 +

x

~|

+

2

2

+

y

F

x; y; z

yz

xz

k:

F

(x; y) = (2x + 5y)~{ + (3x + 2)

~|; L : y = 3x

+ 4x + 1; y = x + 1:

1;

1

1

:

U(x; y; z) = xyz;

M0

; p

3

6

~

2xyz~{ + x

2

z

2

~|

2~

F x; y; z

xyz k:

(

) = z4

y3

+

~

3~

F (x; y; z) =

4

~{ +

3

~| + xz k:

~

2

+ 5x + 2; y = 2x + 1:

F (x; y) = (2x 5y)~{ + (1 3x)~|; L : y = 2x

~

(x; y; z) =

3

3

+

2

2

+ sin

2

~

F

cos

cos

F (x; y; z) = x + y ~{ + 3 x + y ~| 3z x + 2y k:

~

yz

xy~{

xz

xy ~|

~

xy k:

~

(x; y) = (x + 5y)~{ + (2 + 4x)~|; L : y = x

2

+ 5x + 2; y = 2x:

F

2

1

U(x; y; z) = xy2z; M0 1;

; p

:

3

6

~

(

) =

3

3

2

2

2

~

F (x; y; z) = x + y ~{ + 3 x + y ~| 3z x + 2y k:

~

2

3

2

2

2

2

3

~

F x; y; z

2xy

z ~{ + 3x

y

z ~| + 2x

y

z k:

~

4x)~|; L : y = 4x

2

+ 7x + 2; y = 2x + 1:

F (x; y) = (x 5y)~{ + (1

y

1

1

1

U(x; y; z) =

; M0

p

; p

; p

:

xz2

6

6

6

~

~

F (x; y; z) = x (y + z)~{ + y (x + z)~| z (z + x + y) k:

~

~

yz2

1

1

1

U(x; y; z) =

; M0

p

; p

; p

:

x

2

2

3

~

~

F (x; y; z) = x (y z)~{ + y (x z)~| + z (z x y) k:

~

2

~

F (x; y; z) =

4z ~{ + 2y ~| 8xz k:

~

1)~|; L : y = x

2

+ 4x 3; y = x + 3:

F (x; y) = (2y x)~{ + (3x

~

(x; y; z) = z2

2

+ xy

2

2

2

~

F~

~{

~{ x2~| +

xzk:~

zy

k:

F

x; y; z

xy

z

zy ~|

yz

~

(

) =

+ 2

+ + 2

2

+ 4x 2; y = x + 3:

F

(x; y) = (3y x)~{ + (2x + 5)~|; L : y = 2x

~

(

) =

2

2

2

2

2

2

~

F (x; y; z) = y + yz ~{ + z + zx ~| + x + y x k:

~

2

2

2

2

2

2~

F x; y; z

2xy

z ~{ + 2yx

z ~| + 2y

zx k:

~

2

+ 3x + 1; y = 2x + 2:

F (x; y) = (4y + x)~{ + (5x 1)~|; L : y = 2x

~

2

+ (

+ )

2

2

~

F (x; y; z) = (e

+ ye )

F (x; y; z) = x z + 3z ~{ y (x + z)~| + z x z k:

~

y

x

y

x

~

~{

xe

e

~|

z k:

~

x)~{ + (2x + 5)~|; L : y = x

2

+ 3x + 2; y = 4x + 2:

F (x; y) = (4y

~

(

) =

2

2

~

F (x; y; z) =

x z + 3 ~{ +

y 2yxz

~| + (x 2yz) k:

~

~

F x; y; z

(3x + y)~{ + (x

y)~| + (3x + 3) k:

~

2

L : y = x

2

+ 6x + 1; y = 3x + 5:

F (x; y) = (x y)~{ + x ~|;

1: U(x; y; z) = xy2z; M0 1;

3

; p6

:

1

2

1

~

y

x

x

2: F (x; y; z) = (x + 1) e ~{ (y + 1) e ~| + z (e

~

~

3: F (x; y; z) = 3z ~{ + y ~| + (3x

z) k: