Use the Divergence Theorem to calculate the surface integral fSs F · dS; that is, calculate the flux of F across S.= 4x³z i + 4y³zj + 3z4 kF(x,y,z) =S is the sphere with radius R and center the origin. Use Stokes' Theorem to evaluate SSs curl F· dS.F(x,y,z) = x2z2 i + y²z² j + xyz kS is the part of the paraboloid z = x²+y² that lies inside the cylinder x²+y² = 1, oriented upward.

Flux by using Divergence Theorem

Answered: Use the Divergence Theorem to calculate…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let z = g(x, y) = f(3 cos(ry), y + e) provided that f(3, 7) = 4, fi(3,7) = 2, f2(3, 7) = 4. i) Find g, (0, 6). ii) Find 92 (0, 6). ii) Find the equation of the tangent plane to the surface z = f(3 cos(xy), y + e™v) at the point (0,6). Türkçe: f(3, 7) = 4, f1(3, 7) = 2, f2(3, 7) = 4 olmak üzere z = 9(x, y) = f(3 cos(xy), y + e#") %3D olsun. i) 91 (0, 6) değerini bulunuz. ii) 92 (0, 6) değerini bulunuz. iID z = f(3 cos(ry), y + e*") yüzeyine (0, 6) noktasında teğet düzlemin denklemini bulunuz.
Consider a surface defined by F(x, Y, z) = 0 whose gradient is (cos(r2), z² e", 2ze"). The equation of the tangent plane to the surface at the point (-2,0, 1) is O x + y+ 2z -1 = 0 x - y – 2z + 4 = 0 x – z + 3 = 0 O x + y + 2z = 0
Use Stokes' Theorem to calculate the line integral of the vector function F = (y, z, x) along the curve C, which is obtained by the intersection of the surfaces x + y = 2 and x² + y² + z² = 2 ( x + y).
4. Let S is the surface z = 5 - r - y, 1<: in R. Let S be oriented with the normal vector pointing upward direction. (a) Let F(r, y, 2) = (y., z, 3). Use Stokes Theorem to evaluate (b) Verify Stokes' theorem for part (a).
Please explain a, b, and c in a readable way!

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Use the Divergence Theorem to calculate the surface integral fSs F · dS; that is, calculate the flux of F = 4x³z i + 4y³zj + 3z4 k F(x,y,z) = S is the sphere with radius R and center the origin.