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Math Help - Curvature

  1. #1
    Junior Member
    Joined
    Aug 2009
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    25

    Exclamation Curvature

    Find the curvature of r(t) = 3/2 (e^2t + e^-2t)i + 3/2 (e^2t - e^-2t)j + 6tk at t = ln 2

    I think I screwed up somewhere in my calculations.

    I got r'(t) = (3e^2t - 3e^-2t)i + (3e^2t + 3e^-2t)j + 6k
    r"(t) = (6e^2t + 6e^-2t)i + (6e^2t - 6e^-2t)j

    |r'(t) x r"(t)| = 72e^-2t

    |r'(t)| = (18e^4t + 18 e^-4t +36) ^ 3/2

    Those answers just don't look right. Can anyone tell me what I'm doing wrong.
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  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
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    Florida
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    Once you have r ' and r '' go ahead and plug in t =ln(2)

    it will make the calulation a lot simpler

    r ' = (12-3/4) i + (12+3/4) j + 6 k = 45/4 i + 51/4 j + 6k

    etc
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