(c) Use Stoke's theorem to find the circulation of the field F (x, y, z) = (y²)î + (z²)ĵ+ (x²)k around the curve C which is the triangle cut from the plane x + y+z = 1 by the first octant, counterclockwise view from the above. [Hint: do = V3· dxdy = v3 rdrdo.]

Q: 1. Consider the vector field F(r, y) = -y²i+(x+2)j. (a) Evaluate F(0, 1). F(0,1) = (b) Sketch the…

A: Given:

Q: Find the counterclockwise circulation and outward flux of the field F = xyi + 4yʻj around and over…

A:

Q: Calculate the circulation of the field F around the closed curve C. F = y 3i+x2 j; curve C is the…

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Q: Using Stoke’s theorem, evaluate the circulation of the field F( x, y, z )=x ^2i +2xj+ z ^2k  around…

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Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

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Q: use Green’s Theorem to find the counterclockwisecirculation and outward flux for the field F and…

A: We have given F=x+yi-x2+y2j Curve: Triangle bounded by y=0, x=1 and y=x   Green's Theorem-Normal…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A: To use Green's theorem to find the counterclockwise circulation and outward flux for the field F and…

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A:

Q: 8. The component of the field F= (1,2,3) normal to the plane z = -3x + 3y -1 is (a) 0. (b) –2//19.…

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Q: Consider the following vector field. F(x, y, 2) = (4e* sin(y), 9e' sin(2), 8e" sin(x) (a) Find the…

A: Solve the following

Q: Find the flow of the field F = V(x²ze) once around the ellipse C in which the plane x + y + z = 1…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A:

Q: Find the potential function f for the field F. F = (y - z) i + (x + 2y-z)j- (x+ y) k O f(x, y, z) =…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (4x…

A:

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

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Q: find the circulation and flux of the field F aroundand across the closed semicircular path that…

A: The given vector field is Fx,y=-yi+xj.

Q: Calculate the flux of the field F=xi+yj across the closed plane curve C, where C is the closed…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y -…

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Q: Q4// A// Evaluate both side of divergence theorem for the field D=2xy.x^+x².y^ C/m2 and the…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: use Green’s Theorem to find the counterclock-wise circulation and outward flux for the field F and…

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Q: 1) For the vector field F(x, y) =−x²'yi + xy²j, find the following: a) Find the 2D curl of this…

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Q: Let F = (y cos 2x)i+(y sin 2x)j+(x²y+z)k. Is there a vector field A such that F = Vx A? ..... Select…

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Q: 6. Consider the vector field F = (-y,x). a. Check if the vector field is conservative. b. Consider…

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Q: 27-28 Use a graph of the vector field F and the curve C to guess whether the line integral of F over…

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Q: 1. Consider the function f (x, y, z) = y- + y² +z? Determine the gradient vector field of f, F =Vf…

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Q: Use the Divergence Theorem to compute the net outward flux of the field F = (- 2x,y, - 2z) across…

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Q: Calculate the flux of the field F across the closed plane curve C. F=x²i+ y²j; the curve C is the…

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Q: Consider the field F(x.y.z) = 1 (x +y) i+1 (x5+y)j+1 (x2 +y2) k. (a) Integrate F.ds around the…

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Q: Let ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2). Show that the clockwise circulation of the field F = ∇ƒ…

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Q: - xy²)i+(eº+ Please compute the work done by the vector field F(x,y) = (sin x+xy x?)j in R?, where C…

A: Given: Fx,y=sinx+xy2i+ey+x22j C is a path goes around the unit square twice. To find: Using…

Q: 2.4) Use the divergence theorem to find the outward flux of the vector field F(x, y, x) = x³i+ y³j+…

A: The divergence of the given vector field is  ∇·F=∂∂xx3+∂∂yy3+∂∂zz3=3x2+3y2+3z2 Let, S be the surface…

Q: Calculate the work done by the field F when the object moves along the given path from the initial…

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Q: Calculate the flux of the field F=xi+yj across the closed plane curve C, where C is the closed…

A: theory: graph:

Q: Use Green's theorem to find the counterclockwise circulation and outward flux for the field F =…

A: F=(y3-ey sinx) i + (y3+ey cos x) jr2=sin(2θ) we have to calculate the counterclockwise circulation…

Q: 18. F = 1 + i + (tan' y)j x² + y? = 1

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Q: Calculate the circulation of the field F around the closed curve C. Circulation means line integral…

A: Please check your options.

Q: 1. Use Green's Theorem to find the counterclockwise circulation of the field F around the curve C as…

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Q: Find the circulation of the field F = -2xi-2yj around the closed semicircular path that consists of…

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Q: Calculate the circulation of the field F around the closed curve C. Circulation means line integral…

A:

Q: Apply Green’s theorem to find the outward flux for the field F =tan^−1?(y?/x)i+ln(x^2+y^2)j and…

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Q: Problem #4: Use the divergence theorem to find the outward flux F.n dS of the vector field F =…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: 6. Use Green's Theorem to find the counterclockwise circulation and the outward flux for the field F…

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Q: Obtain the circulation integral of the field F = (x+eªseny)î + (x + e* cosy) in the curve C defined…

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Q: 3. For the vector Field E = -(x² + 2y²)âx + (xy)ŷ calculate E dl around the triangular contour (V×…

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Q: 25. Evaluate |F•T ds for the vector field F = x²i – yj along the curve x = y? from (4, 2) to (1,–1).

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Q: Q4: A- Find the flux of the field F = i+j+k √√x² + y² +2² bounded below by the plane z-0 and bounded…

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