Divergence Theorem for more general regions Use the DivergenceTheorem to compute the net outward flux of the following vectorfields across the boundary of the given regions D. F = ⟨x, 2y, 3z⟩; D is the region between the cylindersx2 + y2 = 1 and x2 + y2 = 4, for 0 ≤ z ≤ 8.

Q: 1. F(г, у) (x+ y)i+ ( – y) j - 2. F(x, y) = (x – y) i+ (x + y)j - 3. F(x, у) yi+ cos x j 4. F(x, у)…

A: Please check step 2 for the solution.!

Q: Divergence Theorem

A: and S is the surface of the cube.[-1,1][-1,1][-1,1]

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Exercice 1: On considère le signal suivant ayant pour période 2π. [u(t) = sin(t) u(t)=0 si te [0,7 […

A: Step 1:

Q: Divergence Theorem for more general regions Use the DivergenceTheorem to compute the net outward…

A: Divergence Theorem for more general regions

Q: A normal vector to the tangent plane for the at the point (1, 1, 1) is: y surface x =

A: A(1, 1, 1)z= xyf(x,y,z) =xy-zfx=yfy=xfz=-1Normal vector to the tangent plane for the surface;n^…

Q: Use the definition of the divergence to show that div(c, F, + c2F;) = c, div(F,) + cz div(F,) for…

A: F1, F2 : D ➡️ R3 are differentiable vector fields and for constant c1 and c2 we have to prove that…

Q: Let F(x, y) = (xy² + 7x, x²y-7y). Compute the flux F nds of F across a simple closed curve that is…

A: It is given that the vector field is . Let  then wehave,  and .We have to compute the flux  of the…

Q: F. Sketch the region onto which the sector r ≤ 1,0 ≤ 0 ≤/4 is mapped by the transfor- mation (a) w =…

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Q: Find a vector-valued function, using the given parameter, to represent the intersection of the…

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Q: vardate both sides of the Divergence theorem, where vector F = x ax +y ay +z az, and the closed…

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Q: Q.3) Use the divergence theorem to find the outward flux of the vector field F(r, y, r) = ri %3!…

A: Here, Fx,y,x=xi

Q: 4. Match the vector fields given below with their plots. (a) F(x,y, z) = (b) F(x, y, z) = (c) F(x,…

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Q: F. Refer to the figure where the gradient vectors of z = f(x,y) are plotted. Are A and B constrained…

A: We are given the figure of the gradient vectors of z=f(x, y).

Q: Compute the curl of the following vector V defined by V(x,y,z) = e(x²+y² +z²) y

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Q: Use Green's theorem to find the flux and circulation for the vector field: f(x, y) (2x+ y)i+(x +y)j…

A: Given fx,y=2x+yi+x2+y2j. To evaluate the flux and circulation for the vector field across and around…

Q: Consider the vector field F = (y, –x, x² + y²). Find the flux of F through S if: (a) S the part of…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: (x, y, z) = ( i i

A: Given that Length of vector = 6√3 We have to find component of vector.

Q: a)V=y?? +z²j+x?K bv-x3-xをK 2.

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Q: b) The tangent subspace Wp at p ES is the plane through 0 with normal vector p. Find an explicit…

A: b) The tangent subspace at a point p on the unit sphere is the plane through the origin with normal…

Q: Use the Divergence Theorem to compute the net outward flux of the vector Beld F(x-yr) across the…

A: Let F be a vector field, then by divergence theorem ∬SF→⋅dS→=∭Vdiv(F→)dV