MAT-2130 Midterm: MATH 2130 App State summer2014 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 m (cid:18)zc z ds(cid:19) / no: (14 points) parameterization, arc length, and a line integral. (a) let c be the upper-half of the circle x2 + y2 = 9. Parameterize c and then nd its arc length using an integral. It will only end in tears. ] (b) find the curvature of r(t): (12 points) find the tnb-frame for r(t) = h 2 cos(t), 2 cos(t), 2 sin(t)i. Why or why not: (12 points) no numbers here. Choose one of the following: let be a line parameterized by r(t) = x0 + vt. let x be some point (not necessarily on this line). |v| is the distance from x to the line . Suppose a and b have the same length. Show that a + b and a b are orthogonal.
