MATH 246 Midterm: Exam 2 Solutions Spring 2001
14 Mar 2019
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Show all work in a clear and concise manner to get maximum credit. Circle your answers: consider a wire in space parametrized by. ~c(t) =< 3t, t2, 2t2 >, 0 t 1 : (10 points) set up, but do not evaluate, the integral for the arc length of the wire. ~c (t) =< 3, 2t, 4t >, |~c (t)| = 9 + 20t2, so ds = 9 + 20t2 dt, l = z 1. 9 + 20t2 dt : (10 points) suppose the density of the wire at a point (x, y, z) is (x, y, z) = x. 2 27) : (15points) let ~f (x, y, z) =< exyz, exz + 2yz, exy + y2 + 1 >. ~f is conservative, i. e, = exyz + y2z + z is a potential function for ~f so. ~f d~s where ~c(t) =< cos t, sin t, t >, 0 t . 2: consider the double integral r 1.
