1. Find the point on the curve r{f) = (2 cosf, 2 sinf, (it), 0 g f 3 7r, where the tangent line is parallel to the plane x + y = 1. 2. At what point do the curves r1(t) = (t, 1 t, 3 +122) and r2(s) = (3 .5', s 2, 32) intersect? Find their angle of intersection correct to the nearest degree. 3. Filul the length of the curve r(t) = 121i + Sta/{j + 39k, (1 5 r. g 1. 4. Reparanletrize the curve 1'0?) 2 (92" cos 2H + 2j + ('2' sin 2fk with respect to arc length measured from the point t = [l in the direction of increasing 1?. . Find a parametric representatiol'I of the lower half of the ellipsoid 2:172 l 43,2 + 22 = 1. Ci! 6. Find a parametric representation of the part of the plane a z y + 1 that lies inside the cylinder 2 '2 _ :r: +31; 1. 7. Find and sketch the domain of at, 3;) = J: + \"\"121 Jr\" 1:;2. 8. Draw a contour map of x, 3;) 2 111(2;2 + 43:2), showing several level curves. 9. Describe the level surfaces of the function f('.., y, 2:) = 1:2 y2 22. l' _ .H . ll). Determine the set of points at which the function f(:::,y) = Ejl 1s continuous