Problem 4. (25 points) Let C be the curve given by parametric equations x(t) = 1², y(t) = 2t, z(t) = ln t, te (-[infinity], +[infinity]). (a) Find the intersection points of the curve C with the plane z = e. (b) Find an equation of the tangent line to the curve C at the point (e², 2e, 1). (c) Find an equation of the tangent line to the curve C when t = 3. (d) Find the arc length of the curve C when 1 ≤ t ≤e.