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Question Number 34912 by abdo imad last updated on 12/May/18

let f(x,y,z) =(x^2  +y^2 +z^2 )^α      with α∈R  1) calculate Δf  2) find α in order to have Δf=0

letf(x,y,z)=(x2+y2+z2)αwithαR1)calculateΔf2)findαinordertohaveΔf=0

Answered by tanmay.chaudhury50@gmail.com last updated on 13/May/18

△f=df(x,y.z)  =((∂∫/∂x))_(y,z) dx+((∂f/∂y))_(x,z) dy+((∂f/∂z))_(x,y) dz  =α.(x^2 +y^2 +z^2 )^(α−1) .2x.dx+  α.(x^2 +y^2 +z^2 )^(α−1) .2y+α.(x^2 +y^2 +z^2 )^(α−1) 2z

f=df(x,y.z)=(x)y,zdx+(fy)x,zdy+(fz)x,ydz=α.(x2+y2+z2)α1.2x.dx+α.(x2+y2+z2)α1.2y+α.(x2+y2+z2)α12z

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