MAT-2130 Midterm: MATH 2130 App State summer2015 Test2 answer key
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|r (t)| (cid:19) t(t) +(cid:18) |r (t) r (t)| r (t) = (cid:18) r (t) r (t) x ds,zc y ds,zc z ds(cid:19) / no: (12 points) parameterization, arc length, and a line integral. (a) let c be the upper-half of the circle x2 + y2 = 4. [hint: take advantage of geometry and symmetry. : (15 points) let c be parameterized by r(t) = hsin(t), t3, eti where 3 t 1. (a) set up the line integral rc(x2ey + 4z) ds. It will only end in tears. ] (b) find the curvature of r(t). (c) find the tangential and normal components of acceleration for r(t): (12 points) find the tnb-frame for r(t) = h4 sin(t), 4 cos(t), 3ti. Why or why not: (12 points) no numbers here. Choose one of the following: suppose that |r(t)| = c (the length of r(t) is constant). Suppose that a and b are unit vectors. Prove that (a b)2 + |a b|2 = 1.
