Questions Determine whether or not the vector field is conservative. If it is conservative, find a...

Questions Determine whether or not the vector field is conservative. If it is conservative, find a vector f f such that . F→=∇f. → F ( x , y , z ) =< y cos x y, x cos x y , − sin z > F→ conservative. A potential function for → F F→ is f ( x , y , z ) = f(x,y,z)= + K. (Type "DNE" if → F F→ is not conservative.)

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milcah answered 2 years ago

Question 3. Determine if the following vector fields are conservative. If they are,find their potential functions....

Question 3. Determine if the following vector fields are conservative. If they are,find their potential functions. a.F=〈y,x+z,−y〉. b.F=〈y+z,x+z,x+y〉.

For each of the following vector fields F, decide whether it is conservative or not by...

For each of the following vector fields F, decide whether it is conservative or not by computing curl F. Type in a potential function f (that is, ∇f=F). Assume the potential function has a value of zero at the origin. If the vector field is not conservative, type N. A. F(x,y)=(−14x−6y)i+(−6x+6y)j f(x,y)= C. F(x,y,z)=−7xi−6yj+k f(x,y,z)= D. F(x,y)=(−7siny)i+(−12y−7xcosy)j f(x,y)= E. F(x,y,z)=−7x^2i−6y^2j+3z^2k f(x,y,z)=

For each of the following vector fields F , decide whether it is conservative or not...

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(10x+7y)i+(7x+10y)jF(x,y)=(10x+7y)i+(7x+10y)j f(x,y)=f(x,y)= B. F(x,y)=5yi+6xjF(x,y)=5yi+6xj f(x,y)=f(x,y)= C. F(x,y,z)=5xi+6yj+kF(x,y,z)=5xi+6yj+k f(x,y,z)=f(x,y,z)= D. F(x,y)=(5siny)i+(14y+5xcosy)jF(x,y)=(5sin⁡y)i+(14y+5xcos⁡y)j f(x,y)=f(x,y)= E. F(x,y,z)=5x2i+7y2j+5z2k

For each of the following vector fields F , decide whether it is conservative or not...

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). If it is not conservative, type N. A. F(x,y)=(−4x+5y)i+(5x+16y)j f(x,y)= ? B. F(x,y)=−2yi−1xj f(x,y)= ? C. F(x,y,z)=−2xi−1yj+k f(x,y,z)= ? D. F(x,y)=(−2siny)i+(10y−2xcosy)j f(x,y)= ? E. F(x,y,z)=−2x2i+5y2j+8z2k f(x,y,z)= ? Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"

a) show that the vector field F= <siny, xcosy, -sinz> is conservative by finding a scalar...

a) show that the vector field F= <siny, xcosy, -sinz> is conservative by finding a scalar f such that ∇f=F. b) use this fact to ecaluate ∫C F•dr along the given curve C where C is the line segment from (0,0,0) to (4, π/2, π/2).

Given the following vector force field, F, is conservative: F(x,y)=(2x2y4+x)i+(2x4y3+y)j, determine the work done subject to...

Given the following vector force field, F, is conservative: F(x,y)=(2x2y4+x)i+(2x4y3+y)j, determine the work done subject to the force while traveling along any piecewise smooth curve from (-2,1) to (-1,0)

Determine an example of a vector field that would yield a positive value for a line...

Determine an example of a vector field that would yield a positive value for a line integral around a circle that is traversed once clockwise for any nonzero radius and explain how you know your vector field is correct.

Find the flux of the vector field F = x i + e2x j + z ...

Find the flux of the vector field F = x i + e2x j + z k through the surface S given by that portion of the plane 2x + y + 8z = 7 in the first octant, oriented upward.

QUESTION: In each part, find a formula for a vector field consistent with the description. Provide...

QUESTION: In each part, find a formula for a vector field consistent with the description. Provide at least one numeric example showing the consistency of the formula and the description (an example follows the descriptions). 1.All vectors are parallel to the x-axis and all vectors on a vertical line have the same magnitude. 2.All vectors point toward the origin and have constant length. 3.All vectors are of unit length and are orthogonal to the position vector at that point.

Find the electric field vector anywhere in the plane of a dipole. Let the charge value...

Find the electric field vector anywhere in the plane of a dipole. Let the charge value on one charge be q. Let them be separated by d. Let the origin be in between them. And say they are each on the y axis. Please include a diagram in your answer

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Questions Determine whether or not the vector field is conservative. If it is conservative, find a...

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