MATH 227 Study Guide - Midterm Guide: Or Books, Stationary Point, Simply Connected Space
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Justify all of your answers (except as otherwise speci ed). Let x : [1, 2] r3 be de ned by: x(t) = (cid:18) t2. 3(cid:19) . (a) compute the arc length of the path x from x(1) to x(t) for all. 1 t 2. (b) find an explicit reparametrization of x by arc length. Which of the following subsets of r3 is simply connected? (note that such a set need not be open). Let cr(p) denote the circle of radius r centered at p r2, oriented counterclockwise. Let f = (m, n ) be a c 1 vector eld on r2 such that n points except possibly (0, 0), (0, 2) and (0, 2). Find in terms of , and . Let c1 be the oriented straight line from (0, 0, 0) to (0, 1, 0). Let c2 be the oriented straight line from (0, 1, 0) to (1, 0, 1).
