Consider the conservative force field F = (18x²y+9-y)i + x(6x² - 1)j. Find a function f(x,y) such that F = Vƒ. f = Use this result to find the work done if this force field moves an object from the point (-2,2) along the piecewise linear path to (-1,2), and from there to ( Work =

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

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Q: Find the directional derivative of the scalar field = x¹y + 4xz at the point (2, -2, 4) along the…

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Q: F(x,y) = x²yi + 3y³x²j Find the integral curves for the vector field Оа. -бу + 1 = C 6ху? b. -6ху —…

A: given vector field Fx,y=x2y i^+3y3x2 j^ claim- find the integral curves for the vector field

Q: Find the mass of a wire that lies along the curve r(t)= (t² – 8) j+2tk, 0≤t≤2, if the 3 density is…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

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

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Q: Sketch and describe the vector field F (x, y) = (-y,2x)

A: The given vector field is F→x,y=-y,2x A vector field F→ in ℝ2 or ℝ3 is an assignment of a…

Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: -(4,2) use it to evaluate F. dr (1,0)

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Q: Consider the vectorial V=2+ŷ+ 2 z . . function=z²+x²y + y²2 and the gradient operator Please…

A: Given that the vectorial function ψ→=z2 x^+x2 y^+y2 z^ The gradient operator ∇→=x^.∂∂x+y^.∂∂y+z^.∂∂z…

Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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Q: Find the work done when a particle moves along the x-axis from x= 1 to x= 3 under the action of a…

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Q: Compute the work done by the force field F(r, y) = (2, 3r) acting on an object as it moves along the…

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Q: Determine if h(x, y) e* sinyī + e*cosyj is a gradient vector. If so, find f(xy) so that Vf=h(x, y).…

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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 a potential function of the vector field. F(x,y) = (3x²y + 1, x³+2y)

A: we have to find potential function.

Q: The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at…

A: Here we are given that the gradient of f(x,y)=xsin(y2) is the vector field F(x,y)=sin(y2)2xycos(y2)

Q: find the work done by the force field F(x,y) =(2y+x²,x²-2x) acting on an object as it moves along…

A: Given: The force field, Fx,y=2y+x2,x2-2x.   To find: The work done by the given force field acting…

Q: A force field (in newtons) is defined by F(x, y) = [ + + x, 1 x² +1 y³ зав where coordinates x and y…

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Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

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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 potential function f for the field F = 6x i + 6y j + 7z k. A general expression for the…

A: Note: As you have posted multiple question but I will answer first question according to the…