2. (a) Find the divergence and curl of the vector field Ğ(x, y, z) = (x + y + 5z, 4x – 2y², z³ – 3y). (b) Use the result in item 2(a) to determine whether there is a function and z such that x(x, y, z) = x + y + 5z, Oy (x, y, z) 4x – 2y², and of three variables x, ₂(x, y, z) = z³ – 3y. Y, =

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Q: √²³₁(−12xy² + 8x³y + 3)dxdy

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Q: 2) Find the divergence of the vector field F(r, y, z) = (re") i + (ye") j+ (ryz) k %3D

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Q: For all differentiable vector fields v(r) and w(r), use index notation to show that - . - . v × (▼ ×…

A: We have to show .

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Q: magnitude 1.

A: To find : (x0,y0) Given: (x1,y1) = (2,1) Magnitude = 1

Q: 1. For each of the following vector fields F(1, y), decide if there is function f(z, y) such that F…

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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: Compute the curl of F = (2xy, x²y + x²).

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Q: Given the vector field F(x, y, z) =(z cos(xz) + ze“ )î +(3y² +1)j+(xcos(xz) + xe )k 4. (a) Find the…

A: Given F→x,y,z=z cosxz+zexzi^+3y2+1j^+x cosxz+xexzk^

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Q: 6. Vector fields V and W are defined by V = (2x – 3y + z, –3x – y + 4z, 4y + z) W = (2x – 4y – 5z,…

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Q: (c) Let F(x, y, z) = x³i+y³j + z³k. Compute the following: (i) V-F (ii) VxF (d) Give one example to…

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A: Curl in Vector CalculusThe curl, denoted by the symbol "∇ ×" (nabla cross), is a fundamental…