Compute the flux of F(r, y, z) = [1,–2, z] through the surface S, which is part of the graph z = f(r, y) = ry, corresponding to the region R given by 0

Q: Suppose S is a smooth surface parametrized by r(u, v) over D = [0, 1] x [0, 1] with ru = and rv = .…

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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 F =   Find the outer flux of F through the surface S that is the portion of the paraboloid z =…

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Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

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Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: 1) Consider the closed surface: z = h – x^2 – y^2, h>0, and z=0. Let F=(x^2,y^2,z^2). Find the flux…

A: Consider the given information: The given surface is  z=h-x2-y2,     h>0z=0 Also F→=x2, y2, z2 To…

Q: Let S be the surface defined by the vector function R(u, v) = (v + 4, 4u - v, uv²). Set up an…

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Q: 16. Use the Divergence Theorem to find the total outward flux of F = xi + 2yj + 3zk across the…

A: We have to use the divergence theorem and find out the outward flux of  F=xi+2yj+3zkAcross the…

Q: 5. Compute the flux of F = (x³, -x³ z², 3y²z) across the positively oriented surface z = 3-x²- y²…

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Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: f(x, y) = x - y“; R is the disk x +y < 1.

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Q: Consider the region, R, bounded by the piecewise smooth curve, C, that goes from (0,0) to (2,0) to…

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Q: Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces.…

A: Step 1:- To find the flux of the vector field F=(x2+y2+z2)3/2(x,y,z)​ through the given square…

Q: Let S be the portion of the surface z=Vy²+1+e* that lies above the region R= {(x,y)ER?:x²+y?s1,y20}…

A: Given the surface is z=y2+1+ex,and R=x,y∈ℝ2|x2+y2≤1,y≥0. Find I=∬SF·ndσ, where F=ye-x,2ex-2z,y.

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: Consider the surface defined by the collection of points (x, y, z) = R³ such that 3xz5 + xy +z = 4.…

A: The solution to the above question is  by using a theorem of calculus.

Q: Compute the upward flux of F across the surface defined by R(u,v) = where 0 ≤ u ≤ 2 and 0 ≤ v ≤ 1.

A: The given surface is Ru, v=&lt;2u, 3v, u2-v2&gt;.......(i), where 0≤u≤2 and 0≤v≤1 and F→x, y,…

Q: ented square v V , (0, 1). The va + 8x² y dy)

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Q: Use the divergence theorem to find the flux of F(x, y, z) = (x+ y²)i + yj +k out of the rectangular…

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Q: Let S be the surface given by x² + y²+2z² = 1, x > 0, y ≥ 0, z ≥ 0. Find the flux of (z, 0, 0)…

A: Step 1:The surface S given by x2+y2+2z2=1 is an ellipsoid, and we are considering the upper half…

Q: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant…

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Q: S,F•dr, and C is the triangle, with Use Stokes Theorem to evaluate where F(x,y; =) = (x+ y² )i+ (vy+…

A: Given: Fx,y,z=(x+y2)i+y+z2j+z+x2k and C is the triangle with vertices 1,0,0 ,0,1,0 and 0,0,1 We know…

Q: Find the centroid (ã, j) of the region bounded by: y = 8x? + 5x, y= 0, x = 0, and x = 1 6. x= y =

A: Given equations,  y=8x2 + 5x, y = 0, x =0 and x =1. First of all let us find area of the region…

Q: N z=y+ =2-hx2 x=0 - z=4-y

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Q: Find the linearization L(r. y, 2) of the function f(r, y. 2) = y² sin(2rz) at Po = (7,2.4). Then…

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Q: (x², y², z(x² + y²)) around any closed curve on the surface of Show that the circulation of F = the…

A: Circulation of vector field F around a close curve C = ∫CF.ds If parametric equation of curve C…

Q: 2) Find the outward flux of F across the region D where F(x, y, z) = (In(x² + y²), –tan'(), zVx² +…

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Q: Use divergence theorem to evaluate where F(x, y, z) = 3xi + xyj + 2xzk and s is the surface of the…

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Q: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A: Given: The function is fx,y,z=ex+zy2 and let C be a straight line that will connect the points 4,2,1…