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1. Gabriel's horn. Gabriel's horn is the solid obtained by rotating around the c-axis the infinite region bounded by the curve y = =, the line a = 1 and the r-axis. (a) Find the volume enclosed by Gabriel's horn. (b) It is given that the surface area of Gabriel's horn is given by S = 2T Use a comparison test to determine whether this integral converges or diverges. If it converges, find its value. (c) Explain why the results from parts (a) and (b) are counter-intuitive. 2. (This is problem 17 in section 8.4 of the textbook). The density of oil in a circular oil slick on the surface of the ocean at a distance r meters from the center of the slick is given by o(r) = 50/(1 +r) kg/m. (a) If the slick extends from r = 0 to r = 10, 000m, find a Riemann sum approximationg the total mass of oil in the slick. (b) Find the exact value of the mass of oil in the slick by turning your sum into an integral and evaluating it. (c) Within what distance ~ is half the oil of the slick contained