MATH 317 Midterm: MATH 317 2016 Winter Test 1
Document Summary
Be sure this exam has 12 pages including the cover. Page 2 of 12: a curve in r3 is given by. ~r (t) = (t2, t, t3). (5 pt) (a) Find the parametric equations of the tangent line to the curve at the point p (1, 1, 1). (5 pt) (b) Find an equation for the osculating plane of the curve at the point q(1, 1, 1). Page 3 of 12: a curve in r3 is given by. ~r (t) = (sin t t cos t) + (cos t + t sin t) + t2 k, 0 t < . (6 pt) (a) Find the length of the curve ~r (t) from ~r (0) = (0, 1, 0) to ~r ( ) = ( , 1, 2). (4 pt) (b) Find the curvature of the curve at time t > 0. ~f(x, y, z) = ex sin y + [aex cos y + bz] + cx k.
