Use the extended divergence theorem to compute the total flux of the vector field F(x, y, z) = −3x^2 + 3xz − y, 7y^3 − 6y, 9x^2 + 4z^2 − 3x outward from the region F that lies inside the sphere x^2 + y^2 + z^2 = 25 and outside the solid cylinder x^2 + y^2 = 4 with top at z = 1 and bottom at z = −1.

Q: For the vector field F(x,y) =(2xy²+2y)-i+(2x²y+2x)•j a) show that_F_is conservative vector field; b)…

A: Vector field and integration

Q: Using Gauss' theorem to calculate the flow of the vector field 3x3 F: F (x, y, z) = (x^2z, 2x^2,…

A: As per the question we are given a vector field F(x, y, z) and we have to use Gauss's Theorem to…

Q: - Find the divergence and the curl of the vector fields A = xz³i - 2x²yzj + 2yz¹k B = x²yi - 2xzj +…

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Q: 2) If F(x, y, z) = x²i + y²j + 3zk is a vector field, use Divergence theorem to calculate the…

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Q: Calculate the vector field flux leaving F(x, y, z) = xi + yj + zi solid bounded by the surfaces x² +…

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Q: Consider the vector function F(x, y, z) = x²y² z+ 5xz xz2 -> y3/27 - - -k 4 and calculate the…

A: The divergence of the given vector field is:  2xy2z−2y25​15xz​−2xz​ In case of doubts please do let…

Q: Find curl(curlF→(x,y,z)) of the vector field F→(x,y,z)=x^9zi→−9x^8zj→+yzk→. Enter the exact answer.…

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Q: Let F = (x^2 + y^2, x^2 + y^2) be a vector field and C be the simple closed curve given by circles…

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Q: Find the divergence and curl of the vector field Gir_u_z) = (2t + rosh(ry),2 – sinh y,rz – g xz -…

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Q: The outward flux of the vector field F(x, y, z) = (x, y, z') across the boundary of D- {(x, y. z)…

A: Using divergence theorem calculate the flux:  φ=∯SF.dS   =∰V∇.F.dv…

Q: Let S be the sphere x^(2)+y^(2)+z^(2)=4 with outward normal vector. Use the divergence theorem to…

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Q: Determine whether →F(x,y,z)=3x^2yˆi−yzˆj+zx^2ˆk is a conservative vector field.     Component of…

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Q: Find the work done by the vector field F =( y+x 2, 2%y+z, 2yz + 2) %3D the Curve C ( all over it)…

A: The given vector field is F→=y2+xz,2xy+z2,2yz+x22 and a vector field F→ connects points 1,-1,-1 to…

Q: Find the curl of the vector field F = curl F = i j+ ان اچ k

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Q: Compute the flux of the vector field F(x, y, z) = (2,0, x³) across the portion of the plane x-z = 0,…

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Q: A vector field is given as F=3x²i – yj + z'k a) Find the streamline of the vector field and also the…

A: Streamline of the vector field is the family of curves which are tangent to the vector field. Curl…

Q: Use Divergence Theorem to evaluate the flux integral ∫∫F·ndS, where F = 〈x^2, y^2, z^2〉, S is the…

A: Divergence theorem:∫∫sF.⇀  N^dS =∬∫DdivF⇀dV , here D is the solid bounded by the closed surface S.

Q: Find the total flux of the vector field F= (x^2 z)i + (y^2 z)j+(z^3)k through the closed surface of…

A: Given vector field is  F=x2zi+y2zj+z3k              (i) Given surface is  x2+y2=16z=2z=-2 Let us…

Q: Compute the flux of the vector fields F(x,y, z) = (, y, z) across the 1 and z = 4 whose vertical…

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Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: Let C' be the straight line curve between the points (0,7) and (1,0). Let N be the unit normal…

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Q: Calculate the flux of the vector field (³, ³), out of the annular region between the x² + y² = 9 and…

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Q: Compute the flux of the vector field ♬ = zi +67 through the parameterized surface S' oriented upward…

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Q: disk

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Q: Verify Green’s Theorem for the vector field F(x, y) = (x^2*y^2 , xy) and the closed curve C…

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Q: In a vector field V = (y^a,−x^b,z^c) what is the value of the z-component of curl (V) at (x, y, z) =…

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