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


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

$l e t f (x, y, z) = {(x^{2} + y^{2} + z^{2})}^{α} w i t h α \in R$ $1) c a l c u l a t e Δ f$ $2) f i n d α i n o r d e r t o h a v e Δ f = 0$
	Answered by tanmay.chaudhury50@gmail.com last updated on 13/May/18

	$△ f = d f (x, y . z)$ $= {(\frac{\partial \int}{\partial x})}_{y, z} d x + {(\frac{\partial f}{\partial y})}_{x, z} d y + {(\frac{\partial f}{\partial z})}_{x, y} d z$ $= α . {(x^{2} + y^{2} + z^{2})}^{α - 1} . 2 x . d x +$ $α . {(x^{2} + y^{2} + z^{2})}^{α - 1} . 2 y + α . {(x^{2} + y^{2} + z^{2})}^{α - 1} 2 z$
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