Answer all questions.

(c) Use substitution technique to evaluate J xsin (x2 + 5) dx - 6 marks 4a) If f(x)= VI-x, x51 x+1 x>l Find i) lim f(x) (ii) lim f(x) (iii) lim f(x) - 6 mar (b) Find y' if y = tan? (3x+1) - 5 m (c) A window is being built. The top is a semicircle. If there is 12m of framing material - 9 m dimension of the window be to let in the most amount of light? SHOT ON SMART 4 INFINIX CAMERAI (a)Find y' given that y = In(2x + 1) 4 ers+5 - 6 marks b) Evaluate lim = 5x -1 - 4 marks X-+00 2x241 c) Find y' if x' + y = 3xy - 5 marks d) fx'cos ( x) dx - 5 marks 2 a) Find f' given that f(x) = cos' (3x+1) - 6 marks b) Evaluate lim - sin3x-sin 6x - 5 marks X-0 c) A rectangular piece of cardboard is 8m by 5m. Equal square of side x m are cut from each corner and the remainder folded to form an open box. Find the volume of the box in terms of x, and its maximum volume. - 9 marks 3.m) A curve is defined by the function f(x) = x' - 6x - 15x - 1 (i) Find the maximum and minimum turning points. - 7 marks (if) Sketch the graph of the function. - 2 marks (b) Evaluate [' x(x3 + 3) dx - 5 marks SHOT ON SMART 4 INFINIX CAMERA