Question 1 [18 Marks] Let f be the function defined by f (x ) = 1- 2x2 x2 - 1 (a) Determine the vertical and horizontal asymptotes (show all limits). (4) (b) Use the sign pattern for f (x) to determine (i) the interval(s) over which f rises and where it falls; (5) (ii) the local extrema. (c) Use the sign pattern for f to determine (i) where the graph of f is concave up and where it is concave down. (5) (ii) the inflection points (if any) (2) Question 2 [7 Marks] Find the volume of the solid of revolution generated when the region bounded by y = vx -1, y =0 and x - 5 is rotated about the x-axis. [7] Question 3 [6 Marks] Find the exact value of sec(sin (-;)) [6]