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Quiz 4\quad Sept. 29/Oct. 2, 1992\cr
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1. A particle's position is given by
$$\r(t) = (t - \cos(t))\i + (1 - \sin(t))\j + t \k$$
Find the tangential component of its acceleration at any time~$t$.
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2. Find the {\sl points} in space (if any) where the curve defined by
$$\r(t) = (t^2 + 2t) \i + (t^3 + {3\over2}t^2) \j + (t^4 + 4t) \k$$
is not smooth.
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