MATH 317 Study Guide - Midterm Guide: Constant Curvature
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Problem 1. (5 points) (a) consider the parametrized space curve. Find an equation for the normal plane at the point h1, 1, 1i. (b) find the curvature of the curve from (a) as a function of the parameter t. Problem 3. (6 points) (a) consider the vector eld. ~f (x, y, z) = hz + ey, xey ez sin y, 1 + x + ez cos yi . Is ~f conservative? (b) find the integral rc parametrization. ~f d~r of the eld ~f from (a) where c is the curve with. ~r(t) = ht2, sin t, cos2 ti , where t ranges from 0 to . Problem 4. (6 points) (a) consider the vector eld ~f (x, y, z) = hz2, x2, y2i in r3. ~f d~r, where c is the curve conisting of the three line segments, The surface this curve c surrounds inside the plane x + y + z = 2 has area 3.
