Why should the graphs of f(x,y)= (x^2)+(y^2) and g(x,y)= (-x^2)-(y^2)+(xy^3) be called "tangent" at (0,0)?

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Beverley SmithLv2

19 Oct 2019

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Let g(x,y) = (xy)^(1/3)

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e) Does the graph of z = g(x,y) have a tangent plane at (0,0)? Youmight consider creating a graph of this surface.
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Find a formula F =â© F1(x,y), F2(x,y) âªFâ=â© F1(x,y), F2(x,y) âª for the vector field in the plane that has the properties that F (0,0)=â©0,0âªFâ(0,0)=â©0,0âª and that at any other point (a,b)â (0,0)(a,b)â (0,0) the vector field Fâ is tangent to the circle x^2+y^2=a^2+b^2 and points in the counterclockwise direction with magnitude âF (a,b)â=5sqrt(a^2+b^2).

Consider the lim as x,y approaches (0,0) (x^2+y^2)/xy

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Why should the graphs of f(x,y)= (x^2)+(y^2) and g(x,y)= (-x^2)-(y^2)+(xy^3) be called "tangent" at (0,0)?

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Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

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