find all values of x and y such that f.(r, y) = 0 and f,(x, y) = 0 simultaneously. f(x, y) = x² + 4xy + y² – 4x + 16y + 3

Q: Consider the function f(x, y) = In(x² + y² + 1). 2 (a) Find Vf(1, 2). (b) Find Daf(1, 2) in the…

A: f(x,y)=ln(x2+y2+1) (a)Gradient vector…

Q: Find all values of x and y such that fx(x, y) = 0 and fy(x, y) = 0 simultaneously f(x, y) = x2 + xy…

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Q: The continuity equation satisfied by u=x +2y ,v=2x +y .1O u=2x+y, v=x-2y .IIO u=x/y,V3DY/x .III O

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Q: 3. Find V x F for F(x, y, z) = -IZ i+ x² + y² -yz 1² + y² +√x² + y²k.

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Q: The continuity equation satisfied by u=x/y,v3y/x IO u=2x+y, v=x-2y .II O u=x+2y ,v=2x+y.III O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find ∂ w/∂ x at the point (x, y, z) = (2, -1, 1) if w = x2 + y2 + z2, z3 - xy + yz + y3 = 1, and x…

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Q: Find a function f(x, y, z) such that Vƒ = (3z, 4y°,3x).

A: Given that :-       ∇f=3z,4y3,3x  ⇒∇f=3zi^+4y3j^+3xk^  ....(1) Now we know that…

Q: Find V x F for F(x, y, z) = -IZ -yz √₁² + y²² + √²² +2²² =j + √√x² + y²k.

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Q: f(x, y, z) = ln(x² + y² + z²) at the point P(1, 3, 2) in the direction of

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Q: The real part of z=x+iy is y

A: Answer :

Q: f(x,y,z) = xy + yz + zx, (2, - 2, - 1), A = 3i + 2j - 6k

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Q: Find all values of x and y such that Py(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x.y) = 2x2 - 4xy…

A: Topic = Derivative

Q: F = [r. -x, 0]. = [y. -X, S: 3r + 2y + := 6, x2 0, v 2 0, z 2 0

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Q: Given f(x, y) = 3® – 3xy - 2y, find fz(x, y) =| fy(x, y) = %3D

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Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: Find the extrema points of f(x,y) =x3+6x2+3y2-

A: Given, fx,y=x3+6x2+3y2-12xy+9x Partially differentiate fx,y with respect to x: fx=∂f∂x=3x2+12x-12y+9…

Q: Find Vf at the given point. f(x,y,z) = x² + y² - 4z²+zlnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Topic:- application of derivatives

Q: Solve by theorems of linearity and translation. f(t) = cos t + sin t

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Q: f(x, y) = 3x2 +y+ z Find fx at (0,1,1) %3D 1) 0 2) 1 3) 3 4)-1

A: Given: fx,y=3x2+y+z For finding partial derivative of given function with respect to x, we assume y…

Q: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: 3. Find V x F for F(x, y, z)= -x2 i + x² + y² -yz x² + y² =j+√x² + y²k.

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Q: Find values of x and y such that both f,(x,y)= 0 and fy (x.y)=D0. f(x.y) =x + xy +y² - 3x+2

A: Given that, the function is fx,y=x2+xy+y2-3x+2. Obtain the value of fxx,y.…

Q: Given f(x,y,z) = x³yz². Find fy(1,1,1)

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Q: lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

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Q: Q8) Find the Linearization f(x.y.z) = x² + xy + yz +? at (1,1,2)

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Q: Find fy, fy, and f, for f(x,y,z) = 4xy + 6xz + 2yz.

A: Given, f(x,y,z)=4xy+6xz+2yz

Q: Q: If u =f(x² +2yz, y² + 2=x)Prove that (y-ax

A: Step by step compute the derivative with respect to each variable x,y or z. Then substitute it in…

Q: Find all values of x and y such that Px(x,y) = 0 and Py(x,y) = 0 simultaneously. P(x,y) = 5x²2 -…

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Q: Let f(x, y) = x² + xy + y² where x = 3(t + s) and y = e2st, find . as

A: we have given f(x, y) where x and y are function of s and t.  We have to find the partial derivative…

Q: Let F(x, y) = xy + 2y² + 20x + 6y + 33. Find all values of y such that F(y, y) = –2.

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Q: Find f,, fy, and f, for f(x,y,z)= 5xy+ 3xz + yz.

A: It is partial derivative

Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: 3. Find V x F for F(x, y, z) = -xZ x² + y² i+ -yz x² + y² =j+ x² + y²k.

A:

Q: Find the linearization of f(x,y) at the indicated point (Xo,Yo). f(x,y) = /x +2y; (4,7) L(x,y) =

A: Given:- f(x, y) =√x+2y To find:- linearization of f(x,y) at the indicated point (xo.Yo). f(x,y)=√√x…

Q: ( a) 2.xdV where E = {(x, y,z) |0 < y < 2, 0 <xs/4- y² ,0 < z< y } E

A: As per Bartleby's answering guidelines, we are supposed to answer one question if more than one has…

Q: Find div F if F(x, y, z) = (x² + y) i + z² j + (ey - z) k. 2x - 1 O 2xy i +k O 2x i -k 2хy - 1

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Q: dz and Use the chain rule to find du for z = 4x?y3 – 2x² + 3y where x = uv and y = u –- v

A: Given, z=4x2y3-2x2+3ywherex=uv and y=u-v

Q: Find the linear approximation to the equation f(x, y) xy at the point (4,8,4), and use it to…

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Q: Find a formulaforvectorfield F= M(x,y)i+ N(x,y)j given the fact that for all points(x,y), Fpoints…

A: We have to solve given problem;

Q: Maximize utility U(x, y, z) = 24yz +16xy +16xz Subject to G (x, y, z) = xyz= 384

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Q: Find all functions f(x, y, z) such that grad f = 2xi + zj + yk.

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Q: Find real numbers x, y and z such that (а) (b) 7xi + (y – 3)j + 6k = 10i + 8j – 3zk (x + 4)i + (y–…

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Q: Find the values of ∂z/∂x and ∂z/∂y at the points z3 - xy + yz + y3 - 2 = 0, (1, 1, 1)

A: Given: z3-xy+yz+y3-2=0  At the points (1,1,1) To find: The values  of ∂z∂x and ∂z∂y.

Q: z=f(x,y)=x^4-3xy+1 and x=2t, y=t^3 find dzdt using the chain rule

A: Given query is to find the derivative using chain rule.

Q: Find the minimum and maximum values of f(x,v) = x2 - 3y + y³, x² +4y? < 36

A: Given,         f(x,y)=x2-3y+y3  and   x2+4y2≤36.

Q: f(z) = (x²+y)+i(y²-x) is analytic %3D

A: We have, fz=x2+y+iy2-x Compare the equation with fz=u+iv we will get u=x2+y and v=y2-x Now,…

Q: The Linear approximation (linearization) of f(x) = at x = 2 is %3D (A) y3D -류(z-1) (B) y = - (x – 2)…

A: Given