Consider the path x:R → R2, x(t) = (t2, t3 − t).
(a) Show that this path intersects itself, that is, that there are numbers t1 and t2 such that x(t1) = x(t2).
(b) At the point where the path intersects itself, it makes sense to say that the image curve has two tangent lines. What is the angle between these tangent lines?
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