Given the conservative vector field, F=(x +y³)i +(2xy +5)j , evaluate th Q3 integral | F•ds where C is the path, from (1,2), to (3,4) along any curve.

Q: 2. Sketch at least ten arrows in the vector field: F(x,y)=(-2y)i + (x+1)j

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Q: Find the directional derivative of the scalar field = x³y + 4xz at the point (1,-1, 2) along the…

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Q: Sketch the vector field F. F(x, y) = yi + xj √x² + y² 2

A: Given:The vector field  is given by .To Find:We have to sketch the given vector field.

Q: Evaluate the integral curves for the vector field F(x,y) : i – 4xy²j . О a. - 4у — х2 = C 4x2y2 Ob.…

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Q: Sketch the vector field F(x, y)=2i-j and calculate the line integral of along the line segment from…

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

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Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: 9. Sketch the vector field F(x, y) : :(yi — х). Vx? + y?

A: Consider the given filed, Fx,y=1x2+y2yi−xj Further simplify. Fx,y=yx2+y2i-xx2+y2i=〈yx2+y2,-xx2+y2〉

Q: Consider the vector field v(x)=(y/(x^2+y^2))i − (x/(x^2+y^2)) j + 4k. Calculate ∫Cv dr, where C is…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, 4)…

A: As per Bartleby guidelines I have authority to answer only one question. If you want other…

Q: Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along the curve y = x…

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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: Sketch the vector field F(x, y) = xi + yj and calculate the line integral of F along the line…

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Q: Let R be a differentiable vector-valued function such that R'(t) = (3t2, 2tvt2 + 1, 2t + 3) and R(1)…

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Q: 1) Sketch the vector field F. (i) F(r, y) = (ii) F(r,y, 2) = i

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Q: Find the curl of the vector field F =< yx5, xz², zyб curl F = i + 1:0 12

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