MA 227 Midterm: 3-12f-test1
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Show all of your work for full credit. Find i j and i (j k). Find parametric equations of the tangent line to the curve r(t) = (cos( t), t, ln t) at t = 1. Find the curvature of the curve r(t) = (cos t, t, ln t). A particle moves along the curve r(t) = (t3, t, et). Find its velocity, acceleration, speed, and the tangential and normal components of the acceleration at t = 0. A particle moves with acceleration a(t) = (6t, sin t, et). Find its position r(t) if the initial velocity and position are v(0) = (0, 1, 1) and r(0) = (1, 1, 2), respectively. Find the arc length of the curve r(t) = (3t, 4t3/2, 3t2) with 0 t 1. Find the area of the triangle p qr with p (2, 1, 5), q( 1, 3, 4) and r(3, 0, 6).
