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Homework Help: A mix of limits, slope, and vectors

  1. Feb 24, 2010 #1
    1. A moving particle has position (x(t),y(t)) at any time t. The position of the particle at t =1 is (2,6), and the velocity vector at any time t > 0 is given by (1 - (1/(t^2)), 2 + (1/(t^2))).

    The particle approaches a line as t -> infinity. Find the slope of the line. Show the work that leads to your conclusion.

    2. I found that the position vector is <t + (1/t), 2t - (1/t) + 5>

    I decided that the best thing to do was take the limit of y(t) over x(t), and applied L'Hôpital's rule until the equation turned into something tangible. I ended up with the limit as t approaches infinity to be 2. Is that right? Is that the slope of the line? Did I not go far enough or did I do it completely wrong?
  2. jcsd
  3. Feb 24, 2010 #2


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    That looks fine to me. I don't even think you really NEED l'Hopital. Just divide the numerator and denominator of y(t)/x(t) by t and you've got it.
  4. Feb 24, 2010 #3
    yay!!! thanks
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