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Math Help - Help (Parametric Equation)

  1. #1
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    Help (Parametric Equation)

    Ok so my teacher taught us how to do this but now for a question like this. Can someone tell me how to go about this question?

    Find the parametric equations for the surface obtained by rotating the curve y=e^-x, 0 less than or equal to y less than or equal to 2, about the x axis. Thanks again for the help..this site is so helpful!
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  2. #2
    Super Member
    Joined
    Aug 2008
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    Let f(x)=e^{-x}

    First paramaterize the x-direction with just x. Now consider the y and z as just circles in the y-z plane. The equation for y and z would then be:

    y=f(x)\cos(t)

    z=f(x)\sin(t)

    Then the parameterization for the surface of revolution would be:

    \{x,f(x)\cos(t),f(x)\sin(t)\},\quad 0\leq t \leq 2\pi

    and x whatever range you wish.
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