Regular parametrized curves.

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(1) There are several geometric reasons why we choose to work with only regular parametrized curves. Write a short essay to describe a few of those reasons, using examples to illustrate your points.

(2) Show that the curve β(t) = (sin(3t) cos(t),sin(3t) sin(t), 0) is a regular curve. Then find the equation of its tangent line at the time t = π/3.

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