Is W = ((x,y) | xy=0} a subspace of R??

Q: How do you graph the vector field F = ⟨ƒ(x, y), g(x, y)⟩?

A: Given: vector field

Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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Q: Find the normal line for the level surface f(x,y,z) = 3x3 + cos (2y) + ln (2z) = c at the point…

A: f(x,y,z)=3x3+cos(2y)+ln(2z)-c=0Fx=9x2 , Fy=-sin(2y) , Fz=12z×2=1z∇F =<Fx,Fy,Fz >=<9x2,…

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

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Q: Find the gradient fields of the functions g(x, y, z) = xy + yz + xz

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Q: Find the gradient fields of g(x, y, z) = xy + yz + xz

A: Given that, g(x)=xy+yz+xz   We have to find, Gradient Field.   As we know,  grad…

Q: Find the average value of f(x,y)=3xy over the rectangle R with vertices (−1,−2),(1,−2),(−1,0), and…

A: We have given f(x,y)=3xy Rectangle R with vertices (−1,−2),(1,−2),(−1,0), and (1,0).

Q: Find the gradient vector field of f.  f(x, y, z) = 8sqrt(x^2 + y^2 + z^2).

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Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = x°y*2? . F(1, Y, 2) =

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Q: Find the gradient vector field of f(r, y) = In(x + 3y)

A: Solve for the gradient vector

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

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Q: Q. No. 1): Let H ={ h : x* + y s 0.9 + 175 Show that "H" is not subspace of R².

A: Let , V be a vector space. A subset S of V is said to be a subspace of V if : 1) for any a, b ∈S,…

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

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Q: ..Find the Gradient Vector Field for: f (x,y, z) = x²ye/z

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Q: Consider the subspace W of D, given by W = span(sin x, cos x).                         (a) Show that…

A: Given Subspace W=span(sin x, cos x) of D{space of all differentiable functions} B={sin x, cos x}

Q: Find the total differential of W = x^4 y^3 z^2 + x^3 Y^2 + x^2 z +y + 3 at (2,1,1)

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Q: Find the gradient vector field of f бу f(x, у, 2) = X COS Z (бху) (6y бу -sin бх -sin бу i cos k…

A: Given,

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: Determine if the vector field F=(yz,xz,xy) is conservative?

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Q: find laplace of f(x,y,z)=2x3y2z2

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Q: Explain why the vector field ∇(xy + xz - yz) is conservative.

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Q: Find the gradient vector field of f(x, y) = x°y*

A: Given,          The gradient vector field of fx,y=x5y4.We know that,          The gradient vector…

Q: Find the gradient vector field of f(x, y, z) 5x+ 2y+8z

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Q: Find the gradient vector field of f(x,y) = In(x + 5y). 1 -i+ x + 5y 1. x + 5y 1 -i+ x + 5y 1 j x +…

A: We have to solve

Q: Find the gradient vector field of f(r,y, z) = x*y* +y³z³ + æz°.

A: The gradient vector field of f(x,y,z) is given by ∇f=∂∂xf(x,y,z) i^+∂∂yf(x,y,z) j^+∂∂zf(x,y,z) k^…

Q: Find the gradient field associated with the function φ(x, y, z) = xyz.

A: To find the gradient field associated with the function  φ(x, y, z) = xyz.

Q: + (xytl) Determine the Linearity of this DE. * ya dy y dy O Linear O Non-Linear

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Q: calculate div(F) and curl(F). F = (xy, yz, y² – x³)

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Q: Let xbe inner Product and ||x1|=|ly|| = 1 x+y Lix.y ? why?

A: Given that X is an real inner product space. x ,y be two unit vector from X then need to show that…

Q: Find the gradient vector field of f(x, y) = ln(4x + 2y)

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Q: Find the gradient vector field (F(x, y, z)) of f(z, y, z) = e®2z + $y + 2= F(1, y, z) =

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Q: Show that whether the functions sint and cost in the vector space C[-n, 1]of continuous functions on…

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Q: Evaluate the integral curves for the vector field F(x, y) =i -i .

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Q: f(x,y) = 2x3+4y3-3x2-120x-192y+5 Is f(x,y) a curve, vector field, or surface?

A: To check whether it is a curve, vector or surface. f(x,y) = 2x3+4y3-3x2-120x-192y+5

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

A: Given: f(x, y, z) = 9x2 − xy − z2

Q: Find the curl and also the divergence of F(x, y, z) = (x²z, e" + zz, xyz)

A: The objective is to find the curl and divergence of Fx,y,z=⟨x2z,ey+xz,xyz⟩ Curl and divergence of…

Q: Find the gradient vector field ∇f of f(x, y) = x2 − 4y.

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

A: Take gradient to solve

Q: Find the gradient vector field of f(x, y) = x° sin(9y). F(x, y) = x°i+ sin(9y)j F(x, y) = 9x°…

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Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) 5zy ze F(1, Y, 2) =

A: Gradient vector field F→(x,y,z) of a function f(x,y,z) is given by,…

Q: Determine the position of the y-centroid of the line from x = 1 to x = 5.

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Q: Consider the set S = yl E R : 4x +6z=7y, x – 13y=0 . Is this a subspace of R ? Explain why or why…

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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 vector field (F(r, y, z)) of f(x, y, z) = x² sin(3yz) F(z, y, 2) = (

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Q: Find the gradient vector field of f. 5y f(x, y, z) = x cos %3D Vf(x, y, z) =

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Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?

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Q: Find the divergence of F. y F(x, y) 2 x* + y x* + y

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Q: Consider the vector space of continuous functions over the interval [-1,1] with the inner product…

A: Given that,