1. The paraboloid z = 4.2 + 4y2 and the cone z = V3.2 + 3y2 intersect at a point P and a closed curve C that does not contain P. Determine the point P and find a smooth vector-valued function r(t) for the curve C. Also, compute the distance between the point P and the point Q on C such that OQ = r(0). 2. Let C be the curve given by the smooth vector valued function r(t) = (cost + sin (, cost - sin (, 5() with domain -0o (0,0) exists and, if it exists, its value. Suppose that its limit exists along the lines y = m.r for all m E R and is equal to lim /(x, mx) = 2. Must the limit lim (I,y) >(0,0) S(x, y) exist? If the limit along a = 0 is also equal to 2, i.e., lim S(x, y) = 2, must the limit lim S(x, y) exist? If so, briefly explain (E,1) >(0,0) why. If not, give a counterexample