Verify that the divergence theorem is true for the vector field F on the region E. Give the flux. F(x, y, z)= xyi+yzj + zxk, E is the solid cylinder x2 + y2 ≤ 81,0 ≤z≤ 3.

Q: What is the converse of the following sentence? If you drive over 65 miles per hour then you will…

A: Statement If you drive over 65 miles per hour then you will get a speeding ticket.

Q: Find the flux of the vector field V(x, y, z) = 3xy²i + 5x²yj + 2z³k out of the unit sphere. Flux =

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Q: Compute the flux of the vector field F = yi + 3j – xzk through the surface S, which is the surface y…

A: We compute the flux of the vector field through the surface.

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: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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Q: Find the curl of the vector fleld F(z, y) = 9ye" i+2ejat the point (-2, 0). Enter an exact answer.…

A: F(x, y)=9y2 ex3 i +2x2 ey jcurl F→=∇×F→curl F→=ijk∂∂x∂∂y∂∂z9y2 ex32x2 ey0         =∂∂x(2x2…

Q: Find the flux of the vector field F = across the part of the plane z = 3 + 2x + 4y above the…

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Q: Consider the vector field given by F(x, y) = (6xy – 152 y)i + (3a? + 3y – 10a°y)j find a function…

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Q: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Find the flux of the vector field V(x, y, z) = 2xy²i+ 5x²yj + 3z³k out of the unit sphere. Flux =

A: Denote the unit sphere by S If the sphere is closed,  then the flux of v(x, y, z) out of S is given…

Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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Q: Consider the vector field F = (2, -3). Let C be the straight line segment oriented from point (3,0)…

A: Given vector field, So,

Q: Calculate vector field F = (2-z²+2-x²)i + (2 · y³ + 4·x)j + (2x²z³+2)k a flux from a box with the…

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Q: Compute the flux of the vector field F 3yi + 4j – 3xzk through the surface S, which is the surface y…

A: We apply formula for finding this

Q: Show that Vx (V.f) = 0 for any vector field f.

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Q: of the vector field Parye" + around the boun 4. and y = 4.

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj + yzk; (3,-9, 9) 15i…

A: To find the curl of the vector field at the given point.;

Q: Consider the curve C from (-2, 0, 1) to (6, 5, 2) and the conservative vector field F(x, y, z) =…

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Q: Compute the flux of the vector field - 5yi + 3j- 5azk through the surface S, which is the surface y…

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Q: Find the curl of the vector field F(x, y, z) = x²i – 3j + yz?k. curl F = z?k curl F = z2j curl F =…

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Q: Q.3) Graph the vector field F(x, y) = –yi. Find V.(F × G) where F(x, y, z) = xi – 3j+ zk and G(r, y,…

A: given vector field Fx,y=-yi^  graph of the vector field

Q: Sketch the vector field F(x, y) = 3i + 5j and calculate the flux then the circulation of F| along…

A: (1) The equation of line segment is: x+3-2+3=y-1-5-1=tx+3=t⇒x=t-3y-1=-6t⇒y=-6t+1 The curve…