Let f be the function: X f ( x ) = ( x + 1) 2 for x > -1. (a) Calculate the equation of the normal to the curve f at x = =. Give your answer in the form y = ax + b, where a and b are fractions. [6 marks] (b) Calculate the radius of curvature of the curve f at x = =. Give your answer to 4 decimal places. [6 marks] Let c be a positive constant. The part of the curve f between x = 0 and x = c is rotated around the x-axis to form a solid of revolution. (c) By using the substitution t = x + 1, show that the volume of revolution is: why c+ 1 (c + 1)2 3(c + 1)3 + [5 marks] (d) Let the surface area of the solid of revolution be S. Show that: X (x + 1)2 dx. Using this, conclude that S 2 27(In(c + 1) -1) + +1. [5 marks] (e) What happens to the volume in (c) and surface area in (d) as c goes to infinity? Justify briefly [3 marks]