Realize the Gauss (Divergence) Theorem by considering the volumes (V) given for thevectors below and the surfaces surrounding these volumes .(i) Ã(x, y, z) = yē, – xēy, V:{(x, y, z)|x € (0, 1), y E (0, 1), z € (0, 1)}(ii) Ã(x, y, z)(iii) A(x, y, z) = xēn + yếy + zẽ;, V:{(x, y, z)|x² + y² + z² < 1}(iv) A(x, y, z) = x²ē, + y?ēy + z?E2, V:{(x, y, z)|x² + y² + z² < 1}-= xē, + yēy + zē,, V:{(x, y, 2)|x E (0, 1), y E (0, 1), z E (0, 1)}(v) Ã(p, ø, z) = =ē,,1_V:{(p, ¢, z)\p E (0, 1), ø E (0, 27), z E (-1, 1)}|(vi) Ã(r, 0, 4) =1Er, V:{(x,y, z)|x² + y² + z² < 1}

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(i) Ã(x, y, z) = yē, – xēy, V:{(x, y, z)|æ € (0, 1), y E (0, 1), z € (0, 1)} (ii) A(x, y, z) = xē, + yēy + zē,, V:{(x, Y, 2)|x E (0, 1), y E (0, 1), z E (0, 1)} (iii) A(x, y, z) = xēp + yể, + zēz, V:{(x,y, z)|x² + y² + z² < 1}

(i) Ã(x, y, z) = yē, – xēy, V:{(x, y, z)|æ € (0, 1), y E (0, 1), z € (0, 1)} (ii) A(x, y, z) = xē, + yēy + zē,, V:{(x, Y, 2)|x E (0, 1), y E (0, 1), z E (0, 1)} (iii) A(x, y, z) = xēp + yể, + zēz, V:{(x,y, z)|x² + y² + z² < 1}

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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