APPM 2350 Midterm: appm2350fall2017exam1_sol
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Instructions: electronic devices are not permitted during the exam. On the front of your bluebook, write your name, your instructor"s name, your lecture number, and a grading table for four problems. Start each problem on a new right-hand page. Justify your work clearly and box your nal answer. A correct answer with incorrect or no supporting work may receive no credit, while an incorrect answer with relevant work may receive partial credit: (25 points) Solution: x(t) = 2t and y(t) = (2t)3 will work. (c) determine the unit tangent, t, to the path at the point (2, 8). Solution: using the original r(t) = t i + t3 j we have v(t) = 1 i + 3t2 j and so |v(t)| = p1 + (3t2)2. Evaluating t(t) = v(t)/|v(t)| at t = 2 yields v(t = 2) = 1. 145 ( i + 12 j). (d) determine the unit normal, n, to the path at the point (2, 8).
