Show that the following curve is not closed and that it has exactly one self- intersection γ(t)=(t²-1.t³-t)
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Let be the times where the curve intersects with then and and and Subtracting the x equations gives Since Plugging into the y equations and subtracting gives So the curve intersects itself when t=-1 and t=1 at the point (0,0)
thanks thats nice and easy to understand, my teacher had confused me with his explanation.
Also, note that as t goes to infinity, both and go to infinity but as t goes to negative infinity, [tex]t^2- 1[tex] goes to infinity while goes to negative infinity. That shows that the path is not closed.
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