Assume that all normals of a parametrized curve pass through a fixed point. Prove that the trace of the curve is contained in a circle. | Numerade

SOLVED: Q2: Let C be the curve parametrized by r(t) = (t, cos(t), sin(t)) for 0 < t < 2π. Compute the line integral ∫C F · dr for the vector field F(x, y, z) = (2x 2re^(-zyc), 1).03: Let C be the curve in ℝ² consisting of line segments from (1, 0) to (1, 1), from (1, 1) to (0, 2), and from (0, 2) to (0, 0). Compute the line integral ∫C F · dr for the vector field F(x, y) = (3y sin(y), 1).

SOLVED:In Exercises 5-22, a parametrization is given for a curve. (a) Graph the curve. What are the initial and terminal points, if any? Indicate the direction in which the curve is traced. (b) Find a Cartesian equation for a curve that contains the parametrized curve. What portion of the graph of the Cartesian equation is traced by the parametrized curve? x=3 t, y=9 t^2, -∞<t<∞