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

[mr_coffee]

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!

 

[djeipa]

They are not unit vectors, r(t) is a function of t in 3d space
He wants what ?

 

[Tide]

The two forms are equivalent. Now, can you sketch a graph for each?

 

[mr_coffee]

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

 

[TD]

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

The first one can be written as:

$$\left\{ \begin{gathered}<br /> x = t \hfill \\<br /> y = - t \hfill \\<br /> z = t^2 \hfill \\ <br /> \end{gathered} \right$$

 

[mr_coffee]

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?

 

[djeipa]

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 ?*

 

[TD]

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?

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.

 

[mr_coffee]

TD, this look right?
Here:
http://www.mytempdir.com/1784095
or
http://putfile.com/pic.php?pic=9/27019062888.jpg&s=x4