ху1. Let f(x, y, z) = 2x² + /z? – y² and g(x, y)Answer each of thex²+ y²°following:(i)(ii)(ii)Show that limxy)¬(0,0)g(x, y) does not exist.Find the largest set on which the function f(x, y, z) is continuous.Find the gradient Vf(x,y, z).Find the rate of change of f(x,y, z) = 2x² + /z2 – y² at (2,1, –3)towards the point (1,2,1).Find the direction and magnitude of the maximum rate of change off (x, y, z) at (2,1,-3).Find the level surface of f(x,y, z) passing through the point (2, 1, –3).Find the rate of change of f(x,y, z) along the curve r(t) = 4vt +1ī +e'T +tk.(iv)(v)(vi)(vii)af(viii) Findat& 2 if x(t, s) =t+s,y(t,s) = ts and z(t, s) =Seas

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ху 1. Let f(x, y, z) : = 2x2 + z² – y² and g(x, y) = Answer each of the x²+ y²' following: (i) (ii) Show that limxv)¬(0,0)g(x,y) does not exist. Find the largest set on which the function f(x, y,z) is continuous. Find the gradient Vf(x,y, z). (iii)

ху 1. Let f(x, y, z) : = 2x2 + z² – y² and g(x, y) = Answer each of the x²+ y²' following: (i) (ii) Show that limxv)¬(0,0)g(x,y) does not exist. Find the largest set on which the function f(x, y,z) is continuous. Find the gradient Vf(x,y, z). (iii)

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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