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Calc III< confused on what he wants from directions, graphing a limit?

  1. Sep 28, 2005 #1
    Hello everyone! I have a worksheet and it says Graph the following limits:
    (i) r(t) = <t,-t,t^2>;
    (ii) r(t) = <t,sin t, cos t>

    can that be transformed into a unit vector? like

    r(t) = ti - tj + t^2k?
    &
    r(t) = ti + sin (t) j + cos(t)k

    I'm confused on what he wants!
     
  2. jcsd
  3. Sep 28, 2005 #2
    They are not unit vectors, r(t) is a function of t in 3d space
    He wants what ?
     
  4. Sep 28, 2005 #3

    Tide

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    The two forms are equivalent. Now, can you sketch a graph for each?
     
  5. Sep 28, 2005 #4
    okay i think he wants me to sketch the following space curves:
    (i) r(t) = <t,-t,t^2>;
    (ii) r(t) = <t,sin t, cos t>
    how can i do this? he didn't go over anythig like this
     
  6. Sep 28, 2005 #5

    TD

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    What do you mean 'limits'? It seems to me that these are parametric equations...

    The first one can be written as:

    [tex]\left\{ \begin{gathered}
    x = t \hfill \\
    y = - t \hfill \\
    z = t^2 \hfill \\
    \end{gathered} \right[/tex]
     
  7. Sep 28, 2005 #6
    thanks for the responce, TD... How can i graph that? like can i just do a straight line on x axis, then on y axis, then a parabola on z?
     
  8. Sep 28, 2005 #7
    Find x,y,z relations without t
    Use mathematica or any soft to sketch the figures and asks him *is that what you want Sir ?*
     
  9. Sep 28, 2005 #8

    TD

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    It's something like that yes. Imagine letting t run from small values to larger ones and for each t, the system gives you a point. Looking only in the x-direction, you'll get the standard line x = t, similar for y and in the z-direction, you get the standard parabola.
     
  10. Sep 28, 2005 #9
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