(c) Hence sketch the graph of labelling it with the information obtained in part (b). f, (4) (Note: It is not necessary to find the coordinates of the points where the graph cuts the x-axis.) (Total 13 marks) 8. Let = . Line is the normal to the graph of at the point (4, 2). f(x) L f (a) Show that the equation of is = + 18. L y –4x (4) (b) A is the of Find the of A. x-intercept L. x-coordinate (2) In the diagram below, the shaded region is bounded by the the graph of and the R x-axis, f line L. (c) Find an expression for the area of R. (3) (d) The region is rotated 360° the Find the volume of the solid formed, giving R x-axis. your answer in terms of π. (8) (Total 17 marks)
(c) Hence sketch the graph of f, labelling it with the information obtained in part (b). (4) (Note: It is not necessary to find the coordinates of the points where the graph cuts the x-axis.) (Total 13 marks) 8. Let f(x) = . Line L is the normal to the graph of f at the point (4, 2). (a) Show that the equation of L is y = –4x + 18. (4) (b) A is the x-intercept of L. Find the x-coordinate of A. (2) In the diagram below, the shaded region R is bounded by the x-axis, the graph of f and the line L. (c) Find an expression for the area of R. (3) (d) The region R is rotated 360° the x-axis. Find the volume of the solid formed, giving your answer in terms of π. (8) (Total 17 marks)
semester_1_review.docx