If a curve is defined by parametric equations $x=t, y=e^{-2t}, z=3t-t^3$
and the tangent line at point (0,1,0) is defined by $x=t, y=1-2t, z=3t$,
How would you determine which of the following graphs accurately represent this scenario?
2026-03-26 04:51:57.1774500717
How can you plot a tangent line and curve given the parametric equations for each?
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Here are some hints.
The first and fourth figure show a curve that is bounded in at least two dimensions. Is you curve bounded in any dimension?
In the third, you can see that the curve is quite linear with $x$ or $y$ hanging around $2$. Does your curve do that? Is your curve linear?
The second figure is very poor, but if you can eliminate the other choices, what is left?