#5: Use the divergence F = tan ¹(9y + 4z)i + graphs of z = √x² + y² theorem to find the outward flux JS, F F.ndS of the vector field ₂² ²+2 cosx¡ + √√x² + y² + z² k, where S is the surface of the region bounded by the and x² + y² + z² = 100.

Q: 0) Use divergence theorem to evaluate the outward flux of the vector field F(x, y, z) = r³i+y°j+zk…

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Q: 4. Evaluate the flux of vector field F = zi + 2yj - 2xk across part of the paraboloid z = 4-x² - y²…

A: A vector field F=zi^+2yj^-2xk^ across part of the paraboloid z=4-x2-y2 that lies above the circle…

Q: The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y,…

A: The surface H  is defined by    .The vector field  is given by   .We have to sketch the surface H.

Q: Find the flux of the vector field F(x, y, z) = ri across the outward oriented sphere %3D

A: In this question, we find the flux of the vector field f(x,y,z)=xi The surface is a sphere of radius…

Q: .) Compute the flux of the vector field F = 4x + 4yj through the surface S, which is the part of the…

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Q: (b) Given a potential functionf = Ax-2y³z² + Bx³z² – Cxy, where the coefficients A, B,C, are the…

A: Here A = 0, B = 2 and C = 8

Q: Compute the line integral of the vector field F = (3y, −3x) over the circle x² + y² = 81 oriented…

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Q: Evaluate both sides of the divergence theorem for the vector field D = 2xyx + x²9 [C/m²] and a…

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Q: nt) Compute the flux of the vector field F = 5xi + 5yj through the surface S, which is the part of…

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Q: Consider the vector field F = p? + yzi+ + In(s* + :² + 1)k „j + In(=* + :² + 1)k 12 + y²" defined on…

A: We will use the basic knowledge of vector calculus and integral calculus to answer this question.

Q: Let S be the part of the plane 4x +2y+z=4 which lies in the first octant, oriented upward. Find the…

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Q: (b) In the (x, y)-plane, sketch the vector fields v = (y, 2y, 0) and w = (x−y, x+y, 0), clearly…

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Q: Use Divergence Theorem to find the outward flux of field F = (-5x³ – 5y)i + (yz + 1)j + xyzk through…

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Q: Find the field lines and sketch the field portrait for the following vector fields F : R? → R². (a)…

A: We have to sketch the field portrait for the following vector fields F→:R2→R2. a. F→x,y=xi^+x2j^b.…

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F = (y -…

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Q: #6: [[Finds √x² + y² +²k, where S is the surface of the region bounded by the Use the divergence…

A: The given problem is to find the outward flux of the given vector field over the given surface S of…

Q: Q2) Find the flux of the vector field F(x,y,z) = (x,y, z) , where the surface S is the portion of…

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Q: What is the flux of the vector field (x2,y2,z1 ) through a cuboid with x ranging from 0 to 8.3, y…

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Q: Determine the divergence of these vector fields: (a) P = xʻyz a, + xz a, (b) Q3D p sin фа, + p'za,…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: b) Verify whether the vector field F is conservative, if so, then find the potential function F = (…

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Q: Use the Divergence Theorem to calculate the flux of the vector field F = x²i + y²j + z²k out of the…

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Q: Find the flow of the vector field a = (x + 2y)i + (x + 2z)j − zk along the outer surface of the…

A: Given To find the flow of the vector field a→ = (x+2y)i→+ (x + 2z)j→ - zk→along the outer surface of…

Q: 6. Calculate the divergence of F(7)=ř at the origin (a) Using the geometric definition. (b) Using…

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A: To Specify : The component of a vector field F in R2 where the following conditions are satisfied:…

Q: For the vector field in three-dimensional space F = (4x°y – sin(x – 2))i+ e² v#j– yzk Evaluate…

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Q: Verify Green's Theorem for the vector field F = (y², sin x) and the domain contained inside the…

A: Given Information:The vector field is .Domain of the field is the closed triangular path with…

Q: Let 8. (x2 + y²)%, F = xyz x² + 17 be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}. Find…

A: Given F=8x2+y2, x2+y252, xyz17 is a vector field on U=x, y, z∈ℝ3 | x, y≠0, 0 We will find its curl…

Q: 1: Let Let F = (yz², tan-1(xy), 1 + xy³). %3D a) Show that F is not conservative. b) Show that F…

A: conservative vector field is a vector field that is the gradient of function

Q: The vector field A is given by A = 2r cos(r* + 3y")i + 6y cos(2² + 3y*)j. a) Show that A is…

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Q: Find (a) the divergence and (b) the curl of the vector field F(x, y, z) = cos(z)i + 5ysin(5z)j+…

A: Given vector field is  F(x,y,z)=(cosz)i+5ysin(5z)j+2x2zk

Q: Compute the curl of the vector field F = (xy+ z²,x², xz – 2 curl(F(x, y, z)) = %3D What is the curl…

A: A vector field is irrotational if it is zero at a point.

Q: Find the outward flux of the field F = 8xyi + 4yzj + 2xzk across the surface of the cube cut from…

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