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Unformatted text preview: The tangent plane at ( x ,y ,f ( x ,y )) to the surface z = f ( x,y ) is given by z = f ( x ,y ) + ( ∂f ∂x ( x ,y ) ) ( xx ) + ² ∂f ∂y ( x ,y ) ³ ( yy ). • For g : R n → R m , f : R m → R p , g ( x ) = y , and h ( x ) = f ( g ( x )), D h ( x ) = [ D f ( y )] [ D g ( x )] . • The directional derivative of f : R 3 → R at x in the direction of v is given by D f ( x ) v = ∇ f ( x ) · v . • The tangent plane to the level surface f ( x,y,z ) = k at ( x ,y ,z ) has equation ∇ f ( x ,y ,z ) · ( xx ,yy ,zz ) = 0, provided the gradient is not the zero vector....
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This note was uploaded on 10/11/2011 for the course MATH 20E taught by Professor Enright during the Summer '07 term at UCSD.
 Summer '07
 Enright
 Math, Vector Calculus, Dot Product

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