The particle is at rest when = 1. t Find the velocity of the particle when = 5. t [3 marks] Question 3 Let The graph of is shown below. f The region between = 3 and = 7 is shaded. x x Show that = a. f(–x) –f(x). [1 mark] b. Find the coordinates of the maximum of in terms of f(x) a. [2 marks] c. i. Differentiate loge(x2 + 1) [1 mark] ii. Hence find the area in terms of of the shaded region of giving your answer in the a, f(x), form ln p q.
The particle is at rest when t = 1. Find the velocity of the particle when t = 5. [3 marks] Question 3 Let The graph of f is shown below. The region between x = 3 and x = 7 is shaded. a. Show that f(–x) = –f(x). [1 mark] b. Find the coordinates of the maximum of f(x) in terms of a. [2 marks] c. i. Differentiate loge(x2 + 1) [1 mark] ii. Hence find the area in terms of a, of the shaded region of f(x), giving your answer in the form p ln q.