']], F F(x, y z) = (xy + 2xz)i + (x² + y²)j + (xyz²)k, S is the surface of the solid bounded by the cylinder x2 + y2 = 36 and the planes z = y - 6 and z = 0 Use the divergence theorem to calculate the surface integral F. ds; that is, calculate the flux of F across S.

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: Q) S = the part of the paraboloid z = 10-x^2-y^2 above z = 1 F = [x^3, xy, z] Find the flux of F…

A: Step:-1 Given that S is part of paraboloid z=10-x2-y2 above z=1 Since, given that z=10-x2-y2 and…

Q: Use the Divergence Theorem to find the flux of F(x, y, z) = (x² + y)i+z°j+ (e° – z)k across the…

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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: QI.a) In R",the circular cylinder x+y= 36 is intersected by the plane y +z= 6. find a vector valued…

A: Q.1 (a) we have given that in R3 the right circular cylinder x2+y2=36 by the plane y + z=6  we have…

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 2r + 3y –= 5 be the tangent plane to a surface z = f(r,y) at the point (1,1). (a) Find the…

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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: (a) Compute directly I = S Ss F-dS, where S is the surface of the sphere x? +y? +z? = 4 and F =…

A: X²+y²+z²=4=2² Therefore radius of sphere is 2.

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: Use Divergence theorem to find the outward flux of F = (7x², et², cos³ (y² + x)) of the cube in R³…

A: Given that  and the cube  bounded by the planes The Divergence Theorem

Q: Find the parametrization r(t) = [x(t), y(t), z(t)] of the curve obtained by intersecting the…

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Q: For F(x,y,z) = (6y-4xz/(z2+1)2)i + (-2yz-6x/(z2+1)2)j + (-3/z2+1)k,  Calculate the flux of the disk…

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Q: ve = Vti + Vrj + (2t – 1)k is tangent to the surface x+y-z = 1 Show that the curv when t=l

A: Consider the given curve r=ti+tj+2t-1k And the given surface x2+y2-z=1 First, write the curve in…

Q: Q17// A scalar filed V = x + y exists over a surface S defined by x2 + y2 + z² = 9 bounded by the…

A: Given scalar field is V=x+y The surface S is defined by x2+y2+z2=9 bounded by the plane x=0, y=0,…

Q: A conical domain with vertex (0, 0, b) and axis along the z-axis has as base a disk of radius a in…

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Q: Let z = g(x, y) = f(3 cos(ry), y + e²") provided that f(3,5) = 7, f1(3,5) = 2, f2(3, 5) = 5. i) Find…

A: The function given z=gx,y=f3cosxy,y+exy;f3,5=7,f13,5=2,f23,5=5. i. Find g10,4

Q: tz = g(x, y) = f(3 cos(xy), y + e#") provided that f(3, 7) = 4, f1(3, 7) = 2, (3, 7) = 3. %3D Find…

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Q: Find g, (0,3). ) Find g2 (0, 3). i) Find the equation of the tangent plane to the surface z = f(3…

A: 1st option is correct

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 6) = 7, fi(3, 6) = 2, f2(3,6) = 3. i) Find…

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Q: Let z = g(x, y) = f(3 cos(xy), y+ e#y) provided that f(3,6) = 6, f1(3, 6) = 2, f2(3, 6) = 5. i) Find…

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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: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

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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: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

A:

Q: F (x,y,z) =(2x+ cos(yz) )i +(xe^-z -y)j+ zk vector field D: x^2 + y^2 =4  ,  x+z=2  , z=0…

A: Given vector field is, Fx,y,z=2x+cosyzi+(xe-z-y)j+zk.

Q: b) F(x,y) represents a velocity field of a fluid over a surface S defined by z= 6-3x-2y. If the…

A: The flux over the surface S in the first octant is given by the following integral: Flux=∫SF⋅ndS…

Q: i) Find g1 (0, 4). ii) Find g2 (0, 4). iii) Find the equation of the tangent plane to the surface z…

A: Since g(x, y) = f(3cosxy,y+exy)

Q: Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 7) = 4, fi(3, 7) = 2, f2(3, 7) i) Find g1…

A: