MATH 2D Study Guide - Midterm Guide: Directional Derivative, Talking Lifestyle 1278, Contour Line

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2D
• Professor: All

Document Summary

Winter 2016: let c be the curve de ned by r(t) = (sin t, sin t, 2 cos t) (a) show that the curve c lies on the surface of an ellipsoid and nd the equation of that ellipsoid. Also show that the curve c lies on a plane and nd the equation of that plane. (b) sketch the curve, the ellipsoid, and the plane all in one graph. Use arrows to show the direction of the curve. (c) compute v(t), the velocity vector of c. plot the point r( . 4 ) on your graph in part (b). Use this to con rm velocity vector v( that you got the correct direction in part (b). (d) find the parametric equation of the tangent line to c at the point r( . 4 ): (a) let s1 be the surface de ned by z = x2 + y2. Use z = k traces to sketch s1 in space.