Find the gradient field of the function f(x.y.z) = In 4x + 4y2 +z?. ..... The gradient field is Vf= (Factor completely.) ().

Q: Find the gradient field F = Vo for the potential function o below. P(x,y,z) = In (x2 + 2y2 + z²)…

A: We have to find gradient of given function.

Q: The gradient vector field of for,y)= In +2y) is 2. T True A False

A: The gradient vector field of a function, is defined by the formula below. , where are the partial…

Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

A:

Q: 4. If div F >0 in a region enclosed by a small sphere, the outward flux of the field across the…

A: Given: Divergence F>0 is enclosed by a small sphere in a closed surface . The objective is to…

Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k   a) 65   b) 8x4 + 3y4 + 2z4…

A:

Q: Suppose the field lines of a gradient field F: R2 + R² are hyperbolas and the length of each vector…

A: To find- Suppose the field lines of a gradient field F : ℝ2 → ℝ2 are hyperbolas and the length of…

Q: Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in the…

A:

Q: Find the gradient field of the function, g(x.y,z) = e 22 - In (3x² + 4y²). The gradient field is Vg=…

A:

Q: Find the equation of the gradient vector field for the function f(x, y) = – læ² + 1y and then sketch…

A: The gradient vector field of given function is -2x i + 2y j

Q: For which value of a the field i = (y –x)i +(2x – y)j + azk is solenoidal. Find the gradient of the…

A:

Q: If F (x, y) = x2 i + y2 j is a conservative vector field, find its potential function. With the…

A: The solution are next step is

Q: Find the gradient vector field of the function f. f(x, у, 2) 3 3x соs Vf(x, у, 2) %3D

A:

Q: How do you determine whether a vector field in ℝ2 is conservative(has a potential function w such…

A:

Q: 5. Is the following vector field F(r, y) = (2x – y, -x + 3y?) conservative? If so, find a potential…

A:

Q: Choose a correct potential function for the conservative vector fieldF = (3x-y+1, –x-4y-2).

A:

Q: Show that the field F = (cos x)i + (- y sin y)j + (z3)k is conservative and Önd a potential function…

A: F = ( Cosx )i + ( -y Siny )j + ( z3 )k  F = gradient ( - Sinx - y Siny - Cosy + z4/4 ). Thus, we can…

Q: Find the conservative vector field for the potential function by finding its F(x, y) = x² + 5y2

A:

Q: Find the gradient field of the function, g(x,y,z) = e 3z - In (x +2y).

A: Given function  gx,y,z=e3z-lnx2+2y2                     (1) The gradient field is  ∇g=∂g∂x,∂g∂y,∂g∂z…

Q: of f. Sketch the gradient field for f (x, y) = /x² + y? along with several level curves

A: Here we have,

Q: Find the gradient field F = Vo for the potential function o = x²y-3y²x. F =

A: Given the potential function:φ=x2y-3y2xWe need to find the gradient field F=∇φ

Q: Show that the isoclines of dy/dt= t are vertical lines. Sketch the slope field for −2 ≤ t ≤ 2, −2 ≤…

A:

Q: Explain why a potential function for a conservative vector field is determined up to an additive…

A:

Q: 5. Suppose that the vector field F = is conservative. Find a potential function of the vector field…

A:

Q: (xy³ +3x²y, 3xy² + x²) 2+x ху у,

A: According to question given that Vector Field F⟨xy3+3x2y, 3xy2+x2⟩

Q: Let f(x, y, z) = 3xyz + y?z. Find the gradient field Vf.

A: Formulae of gradient field is given below

Q: Q3) Determine if the vector field F(x, y, z) = (yz,xz + 2y, xy + 1) is conservative. If it is, find…

A:

Q: Find a potential function for the conservative vector field. F(x, y) = xex*4Y(2yi + xj)

A: If curl f is zero then conservative field

Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² –…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k 8x4 + 3y4 + 2z4 O 40x4 + 15y4 +…

A:

Q: Find the gradient fields of the functions ƒ(x, y, z) = ln√(x2 + y2 + z2)

A: The given function is fx,y,z=lnx2+y2+z2   The gradient field of a function is represented by,…

Q: Find the gradient field F = Vq for the potential function o = 3x y-y²x. %3D F = O0

A:

Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…

A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5

Q: Determine if F = (12r – 2x cos y, 2y + x² sin y) is a conservative vector field. If it is, find a…

A: Given that F=(12x3-2xcosy)i+(2y+x2siny)j. We need to determine whether if F is conservative field or…

Q: What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² – k².

A: If z=f(x,y), then the variables x, y are called the input of the function, and z is called the…

Q: Find the gradient vector fields for the following potential functions (a) f(x,y) = x²y – xy?

A:

Q: For what values of b and c will F = (y2 + 2czx)i + y(bx + cz)j + ( y2 + cx2)k be a gradient field?

A: The vector field is F=y2+2czxi+ybx+czj+y2+cx2k. Here, M=y2+2czx, N=ybx+cz+P=y2+cx2

Q: Q1. What is vector field and potential function? Sketch the gradient field of p(x, y) = x² + y² -k².

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Compute the gradient field of f(x, y, z)= e^z + xy^2

A: Take gradient to solve

Q: (a) For any vector field F, the gradient of the divergence of F is always zero.

A: Since the gradient of divergence of F is given by

Q: Find the directional derivative of the field f(x, y, z) = -4x³ + 3 xy² + 5 y³ at P = (-1,–3,5) in…

A: Given f(x,y,z)=-4x3+3xy2+5y3  we have to find directional derivative of f at P=-1,-3,5 in the…

Q: Find the gradient field that corresponds to function (x, y, 2) y x +x e-y z

A: The given function ϕx,y,z=y2-x2+xez2-y3z The gradient of a function is given by ∇f=∂f∂x,∂f∂y,∂f∂z

Q: Find the gradient field F = Vo for the potential function = 2x³y-4y³x.

A: We have to find out gradient

Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

A:

Q: Find the gradient vector field of f. f(x, y) = xe³xy Vf(x, y) =

A:

Q: Which of the following functions is a potential function for the conservative vector field F (x, y,…

A:

Q: Consider the conservative vector field given by: F (x, y) = (x - ycos (x), y - sin (x)) A potential…

A:

Q: Find the gradient field of the function g(x,y,z) = 8xy + 2yz + xz. Vg= (Type your answer in terms of…

A: We have to find the gradient field.

Q: Find the conservative vector field for the given potential function. f(x, y) = 9x2 + 2xy + 10y2 F(x,…

A: