Evaluate the flux integral F-ds where Pis the part of the paraboloid -= 4-x -y above the xy plane oriented upward, and F(x, y,z)=xi+ yj+:k.

Q: Compute the flux of F¹ = 5(x + z)i + 5j + 5zk through the surface S given by y = x² + z², with 0 ≤ y…

A: The given surface is  and .The flux is given by  where  is the vector function that describes the…

Q: Let G = {(x, y): 1 ≤ x^2 + y^2 ≤ 16,0 ≤ y ≤ x). Sketch G, and find the coordinates of its centroid.

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Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The given vector field is F→=xi+yj+zk. The goal is to evaluate the flux or surface integral of the…

Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: Suppose F(x, y) = x*i + yj and C is the line segment segment from point P = (-5, 5) to Q = (-8, 9).…

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Q: Compute the flux of F = xi+yj+zk through the curved surface of the cylinder x² + y² = 1 bounded…

A: The vector field is F=xi^+yj^+zk^. The curves surface is x2+y2=1 bounded below by the plane x+y+z=2…

Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: F(1, y.:)= (x², 2x²y*, 5yz*) Given: Find (a) div F (b) curl F

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Q: Find the flux F(x,y,z)=2xi+2yj+zk across the part of the paraboloid z=4-x^2-y^2 above the xy-plane…

A: We have to find the flux F(x,y,z)=2xi+2yj+zk across the point of the paraboloid z=4-x2-y2 above the…

Q: Give a acalar equation for a plane at distance 6 from the plane P with equation x+2y+2z = 5. 0-0

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Q: The equation for a plane tangent to z = f(x, y) at a point (xo, Yo) is given by z = f(xo, Yo) +…

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Q: Integrate g(x, y, z) = x + y + z over the portion of the plan 2x + 2y + z = 2 that lies in the first…

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Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: C₁: r₁(s) C₂: r₂(t) C3 r3(u) = = = (s 2)i+ (2s² - 1)j + k 2t² i + (3t+7)j + (t+1) k (SER) (t = R)…

A: for the given vector functions for the curves C1,C2 and C3 To answer the given questions.

Q: Calculate % F-dr where

A: Given,           F=xyi+2zj-xykand C is the intersection of the of the plane y=z+2 withcylinder…

Q: Calculate F - dS where F = (e" sin y, e" cos y, yz²) S is the surface of the box bounded by the…

A: Given F¯={exsiny,excosy,yz2)

Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

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Q: Compute the curl of F = (3y2, ay, 22).

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Q: Evaluate the integral // Fn ds where F = (2r+32)i-(rz+y)3+(y² +2)& and S is the surface of the…

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Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: (b) Use Green's theorem to calculate the circulation of F around the triangle with verticcs (2,0),…

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