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Math Help - Find Curvature Question

  1. #1
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    Find Curvature Question

    Find the curvature κ(t) of the parabola x(t) = (t, t^2) for -∞ < t<∞

    I've found d2x/dt2 to be 2 and dx/dt to be 2t

    using κ(t) = d2dt2/(1 + (dx/dt)^2)^3/2
    is there any way I can easily simplify this?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Playthious View Post
    is there any way I can easily simplify this?
    No, there isn't.

    Regards.

    Fernando Revilla
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  3. #3
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    Quote Originally Posted by Playthious View Post
    Find the curvature κ(t) of the parabola x(t) = (t, t^2) for -∞ < t<∞

    I've found d2x/dt2 to be 2 and dx/dt to be 2t

    using κ(t) = d2dt2/(1 + (dx/dt)^2)^3/2
    I assume you mean (d2x/dt2)/(1+ (dx/dt)^2)^2/3 in your notation.

    is there any way I can easily simplify this?
    Well, you could put in the values you got for the first and second derivatives!
    \kappa(t)= \frac{2}{(1+ 4t^2)^{3/2}}
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