ull Zain JO ☺4:47 AMO 66%EE202_HW2_2020_2HomeworkQ1) Determine the gradient of the following scalar fieldV = e(2x+3y) cos5zQ2) Given f = x²y + 3z + 4, find (i) Vf. (ii) V² f, and (iii) a unit normal to f= 0 at (1, -2, 4).Q3) Find the divergence and curl of the following vectors:А 3D еху а, +sinxy a, + cos? xz a,Q4) Given the vector fieldR %3 (2x?у + yz)a, + (ху? — хz")а, + (схуг — 2х?у?)а,Determine the value of e for R to be solenoidal. (Note: solenoidal means the divergence equal tozero)05) If the vector fieldт 3 (аху + Bz3)а, + (3x? — үг)а, + (3xz? — у)а,is irrotational, determine a, B, and y. Find V-T at (2, -1, 0). (Note: irrotational means the curl equalto zero)

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Answered: QI) Determine the gradient of the…

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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QI) Determine the gradient of the following scalar field V = e(2x+3y)cos5z