Problem X MATH 10 X re Lec 10.2, x re EU1 - Ch X calorimet X Ch6Pr38: X Factoring X C Solved: ( X G if det(a) x @ 2023-MA X Course H X + X C eclass.srv.ualberta.ca/pluginfile.php/9159924/mod_tab/content/217164/2023-MATH101-A11.pdf 2023-MATH101-A11.pdf 1 / 1 225% 1. Find the length of the plane curves: ( a) y = for Vet - hat, 0 5 x 5 2, (b) r = cost ("), 0 E [0, 27]. 2. Consider the parametric curve r(t) = (2t2, t - 1, 3 -2), teR. (a) Find parametric equations of the tangent line to the curve at the point (8, 1, -1). (b) Find points on the curve where the tangent line is parallel to the plane x ty + z = 3. (c) Show that the given curve is the curve of intersection of a cylinder and a plane. 3. Consider the parametric curve r(t) = (et cost, et sint, v2et), teR. (a) Show that the curve lies on a cone. Sketch the curve and the cone. (b) Find the length of the arc of the curve from the point (1, 0, v2) to the point (e27, 0, V2e27). (c) Reparametrization with respect to arc length measured from the point (1, 0, v2) in the direction of increasing t. 4. Consider the surfaces z = r2 and tan 0 = 2 given in cylindrical coordinates. 5:27 AM Mostly cloudy Q Search ENG US 2023-04-03