3x²y if (x, y) = (0, 0) + y? if (x, y) = (0, 0) f(x, y) = { x +

Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: f(x, y, z) = 3x - 2y + z- 12 = 0 g(x, y,z) = 4x + 2y - 25 = 0 h(x,y, z) = x- y²z-7= 0

A: Use the following formulae, to find the approximate solution of the non-linear system by the Newton…

Q: xyz 3. If (x, y.2)= In +ef), find f,,f, and f.. 4

A: Given: fx,y,z=lnxyz4+e-3xy2z2 The objective is to find fx, fy and fz

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7. fxy(x,y)=

A: Concept: Partial derivatives: In differential geometry and vector calculus, the partial derivative…

Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

A:

Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: 12. f(x, y) = x' – 2x – y + 4y, P = (1, 2). -

A:

Q: f(x,y)=x² +y° +3xr² – 3y² –8

A: Given f(x,y)=x3+y3+3x2-3y2-8To find critical points, we first compute∂f∂x and ∂f∂y  ,…

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

A:

Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: (d) If F(x, y) = (4x² - y², -2xy), then f(x, y) =

A:

Q: 3. zy if y + x² – 3xz = 222

A:

Q: - 5x + 4y – 3z = - 1 - 10x – 4y – 4z = 46 20x – 4y – z = - 44 (x, y, z) =

A:

Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

A:

Q: I'+yz² -2xyz = f(x*y+y*z+z*x)

A: Given:- x3+yz2-2xyz=fx4y+y4z+z4x

Q: f(x, y) = 2y – 6ry - x 2.

A:

Q: 6 - 3x2 + 3 Find the general antiderivative of f(x) - - - x5 + C

A:

Q: (3x)i + (3y)j + (3z)k F = x3 + y3 + z3

A:

Q: 4) f(x, y,z) = /1– x² – y² – z²

A: Domain is the subset of R3 where the function is defined

Q: a z = 4x³-6x²y²-y com x= 2sen(t) y=-3cos(t) e

A: #As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Find fxy(x,y) if f(x,y) = (x5+y³) 7. fxy(x,y) =

A:

Q: (2xy + 3x²)e, + (x² – 2yz + 2y)e,- (e2 +y²)e, olan f(x,y,z)

A:

Q: GiNen Y+ 3y -22 こ4 what is the value of - - マ+ メと 2y +3z = -1 X +y tz?

A:

Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: f(x,y)=(3x^2+3y^2)

A: Given, f(x, y)=3x2+3y2 BOUNDARY OF A DOMAIN :- It is the set of all boundary points of the domain D.

Q: 2(x-1) + If y = Vx? – 2x then y' 3x2-2x T O F

A:

Q: 2(x-1) + If y = Vx? – 2x then y' %3D | 3Vx2-2x

A: To find the derivative of the given y

Q: z = xy³ – a²y, x = t² + 1, y = t2 – 1

A:

Q: 6x + 17y df f f(x,y) then i : 6x 17y ду 204x (6а — 17у)? - 204x - (бх — 17у)? 204x (6x + 17y)² 204x…

A:

Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

A:

Q: f(x,y) = x +y +8x- 2y

A:

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

A:

Q: 2x +y-z=3 x- y+z=0 y+2z =1. Then x=

A: Given system of linear equations; 2x+y-z= 3 x-y+z = 0    y+2z=1 We can use Cramer's rule to solve…

Q: If 6x° +x*-y? 3x² +y? if (x, y) (0, 0) f(x, y)= if (x, y)= (0, 0) then f,(0, 0)=

A:

Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: 3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

A:

Q: [v= -y +2x ,x' = 4y + x + t

A:

Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

A:

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: ーX + 2y - z= 0 ーX - y + 2z = 0 Z = 1 2x

A:

Q: F(x,y, z) = 5x² + 2y² + 4xy + xz

A:

Q: Мaximize p = 10x + 10y + 15z subject to + z s 12 X y - 2x 2y + z 2 14 -y + z 2 4 x 2 0, y 2 0, z 2…

A:

Q: f (x, y) = x² + 3y² + 4,

A: Supposing the question is asking to find the local minima value.

Q: f(x,y) = x² - xy +y² – 9x + 6y + 10

A:

Q: 2X + y - x - 2y + 2z = -11 3x - y + z = (x, y, z) =

A:

Q: f (x, y) x+ 3 ху 3 Бъ-х

A:

Q: 3 18. z= 19. y= Vx(x-1) 3x-1 20. y= 2x+1

A:

Q: f(x,y) = 3y3 – 2xy + 12y – 3x² – 8x – 16 then fy equals ух

A:

Q: y = (2x + 1)v2x+1

A: