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Math Help - Calculus III Question

  1. #1
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    Calculus III Question

    Let Τ = (t, (1+t)/(t), ((1-t^2)/(t)), t>0, and C=Trace(Τ).
    Show that C lies on the plane Γ with equation: x - y + z +1 = 0

    I got

    T(1) = (1, 2, 0)

    Plugged in:
    x - y + z +1 = 0
    (1-2+0+1) = 0
    0=0

    Then I sketched the graph x - y + z + 1 = 0 in (x,y,z)

    Am I done?
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Calculus III Question

    can you clarify what you mean by Trace?
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  3. #3
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    Re: Calculus III Question

    to sketch Τ = (t, (1+t)/(t), ((1-t^2)/(t)), t>0
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  4. #4
    Senior Member jakncoke's Avatar
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    Re: Calculus III Question

    yes you are done then.
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  5. #5
    Super Member ILikeSerena's Avatar
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    Re: Calculus III Question

    Hi ErikFBueno1990!

    Quote Originally Posted by ErikFBueno1990 View Post
    Let Τ = (t, (1+t)/(t), ((1-t^2)/(t)), t>0, and C=Trace(Τ).
    Show that C lies on the plane Γ with equation: x - y + z +1 = 0

    I got

    T(1) = (1, 2, 0)

    Plugged in:
    x - y + z +1 = 0
    (1-2+0+1) = 0
    0=0

    Then I sketched the graph x - y + z + 1 = 0 in (x,y,z)

    Am I done?
    It seems to me that you have to prove that the curve C lies in the plane Γ.
    To do so for only T(1) would not suffice.
    It would suffice if you also have a tangent that is perpendicular to the plane for every value of t.


    Quote Originally Posted by jakncoke View Post
    can you clarify what you mean by Trace?
    Since C is a common symbol for curve and since T identifies a curve, I'm guessing that it means that C is the curve traced by T.
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