Calculate the work done by the vector field F(x, y)= ,2xy) on a particle that moves once around the closed path C drawn below. y = sin(x) 3n/2

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

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: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: Suppose a particle, whose initial position is (1, 0, 0), moves with velocity given by v(t) = (-1,…

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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: Find the work done by the vector field F = xi + 2xyj + 3xyzk on a particle that moves along

A: Introduction: The size of the region enclosed by the graph of the supplied function between two…

Q: Find the curl of the vector field F = (3y cos(x), 5x sin(y))

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Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+ e*cos(y))j through the right…

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Q: Find the curl of the vector field F (6x sin(y), 2y cos(x)). curl F =

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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: dy Draw the direction field for = y ln(x+y) using MATHEMATICA! dx

A: Solution: The graph of the given slope. dydx = xln(x + y)  Shown below.

Q: Find the curl of the vector field F curl F= (5y cos(x), 2x sin(y)).

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Q: 1. SF ·d† = 0 2. ,F ·dT >0 3. ,F ·dT < 0 4. The value of [, F ·dT cannot be determined with only…

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