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Math Help - Level Curves

  1. #1
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    Level Curves

    The question is draw several labelled level curves for the function
    F(x,y)=1/(x^2+y^2)
    and sketch the graph of its surface.
    Nooo idea where to start. Help!
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  2. #2
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    Quote Originally Posted by calculuskid1 View Post
    The question is draw several labelled level curves for the function
    F(x,y)=1/(x^2+y^2)
    and sketch the graph of its surface.
    Nooo idea where to start. Help!


    Choose c\in\mathbb{R}\Longrightarrow \frac{1}{x^2+y^2}=c\Longleftrightarrow x^2+y^2=\frac{1}{c}\Longrightarrow this means that it must be c> 0 (otherwise you get the empty set) , and for c>0 you get the

    circle with radius \frac{1}{\sqrt{c}} and centered at the origin . These are all the level curves.

    Tonio
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