* Determine whether F is a conservative vector field. If so, find a potential function for it. F(x, y) = x ln yi + y ln x

Q: Determine whether the vector field is conservative, and, if it is, find the potential function. (If…

A: We have to find the potential function

Q: use hokes therom  to caluclate the cisculation of the field                  F=x2 i+2x j+z2k around…

A: To use Stokes theorem to calculate the circulation of the field F=x2 i+2x j+z2k around the the curve…

Q: Show whether or not F is a conservative field. If it is, find a potential function for it and use it…

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Q: Determine whether the vector field is conservative. If it is, find a potential function for the…

A: According to the problem, we get

Q: Determine whether F(x, y) = 4x²y i+ 9xy²j is a conservative vector field. If so, find a potential…

A: Determine whether F(x,y) is a conservative vector??

Q: 3x 3x Determine whether F(x, y) = e³ cos 3y i – e³ sin 3yj is a conservative vector field. If so,…

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Q: 3. а. Given a potential function/- Ax'y*z' - Bx"y'z -Cx'y'z, where the coefficients 4.B.c, are the…

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Q: Determine whether the vector field is conservative. F(x, y) = xe+²2y (2y + xj) conservative O not…

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Q: Determine whether the vector field is conservative. If it is, find a potential function for the…

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Q: Alternative construction of potential functions in ℝ2 Assume the vector field F is conservative on…

A: where k(y) is some function in y

Q: Determine whether the vector field is conservative. If it is, find a potential function for the…

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Q: Determine whether the vector field is conservative. F(x, y) = (7y - x²)i + (7x + y)j conservative…

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Q: Determine whether the vector field is conservative and, if so, find the general potential function.…

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Q: Determine whether the vector field is conservative. If it is, find a potential function for the…

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Q: F Is the vector field protected? Your show. If it is protected, find a potential function for the…

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Q: (a) Is the vector field F(x, y) = (xe³, ye²) conservative? Justify your answer. If it is…

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Q: Determine whether the vector field is conservative. F(x, y) = yi + xj conservative O not…

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

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Q: 6. Given F(x, y, z) = (8x° +z²,-3z, 2xz – 3y), a) Determine whether or notF is a conservative vector…

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Q: Determine whether the vector field is conservative. If it is, find a potential function for the…

A: Vector field F is conservative when curl F=0 Consider  F(x, y)=-yx2i+1xjThencurl F=∇×F…

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: Determine whether the vector field is conservative and, if so, find the general potential function.…

A: If curl of F is zero then F is a conservative vector field

Q: (1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a…

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Q: CoS(E);2Y, -Xsin (e))

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Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = (…

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Q: Determine weather the vector field F is conservative. If it is, find a potential function for the…

A: Remember that curl of the vector field  F=F1i + F2j +F3k is curl F=∂F3∂y-∂F2∂zi-∂F3∂x-∂F1∂zj +…

Q: d) Determine whether the vector field is conservative. If it is, find a potential function for the…

A: Let a vector field is given by,                                  The vector field is conservative…

Q: Find a potential function for the vector field F(x, y) = (6x sin y, 3 cos x ), if it exists. A. No…

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Q: 3. Determine if F = x*yi+ xyz j + x²y² k is a conservative vector field.

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Q: Determine whether F(x, y) = 2x²y i+ 8xy' j is a conservative vector field. If so, find a potential…

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Q: Determine whether the vector field is conservative. F(x, y) = (8y − x2)i + (8x + y)j   If it is,…

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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: determine if the given vector field f is conservative and hence find the potential function for the…

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Q: Determine if F(x, y, z) = (z! + z In y, z + z ln x, y ln x + x In y + z²) is a gradient vector…

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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: a) What is a conservative vector field?(b) What is a potential function?

A: Conservative vector field: A conservative vector field is a vector field that is the gradient of…

Q: Determine whether the vector field is conservative. F(x, y) = xe(x^2)3y(2yi + xj)   If it is, find…

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Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = ,…

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Q: Determine whether the vector field is conservative. If it is, finda potential function for the…

A: Here we need to find first whether F is conservative and then find its potential function f.

Q: 3x cmine whether F(x, y) = e³ª cos 3y i – e³ª sin 3yj is ervative vector field. If so, find a…

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Q: Which graph represents the gradient vector field of f(z,9) = Sz + y

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Q: If 0(x,y) is a potential function for a constant vector field F = (a, b), then the graph of the…

A: The constant vector field is F=a, b. The equation of the function is z=ϕx, y

Q: Determine whether F(x, y) = 6x²y i+ 4xy²j is a conservative vector field. If so, find a potential…

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Q: Given a potential function f = Ax² y° z° + Bx° z° – Cxy , where the coefficients A, B,C , are the…

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Q: Determine if F(x, y, z) = (z2 + z ln y, z2 +z ln x, y ln x + x In y + z2) is a gradient vector…

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Q: Is the vector field protected? Your show. If it is protected, find a potential function for the…

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Q: 14

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Q: Determine whether the vector field is conservative, and, if it is, find the potential function. (If…

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Q: Determine whether the vector field is conservative. 7x², F(x, y) = Yi + conservative O not…

A: If curl f is zero then vector field is conservative otherwise not

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: