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Question Number 74301 by ~blr237~ last updated on 21/Nov/19
ProvethatS={(x,y,z)∈R3∖x2+y2=z2}isasurfaceandfindoutifpossiblethetangentplaninO(0,0,0).
Answered by mind is power last updated on 21/Nov/19
S−{(0,0,0)}isasurfaceletfR3→Rf(x,y,z)=x2+y2−z2⇒S=f−(0)df=(2x,2y,−2z)≠(0,0,0∀(x,y,z)∈R3−{(0,0,0)}⇒fisEmersioninanypointIR3−{(0,0,0)}⇒S−{(0,0,0)}issmothemanifoldoforder2topoligacldefinitionofsurfacesin(0,0,0)gradf=0→
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