Question 3 (a) Interpret lim Ek=16 11 6k n-0o n2 n 3 as a definite integral and evaluate it. (9 marks) (b) For a positive constant k, let g(x) = k In(x - k), defined over the domain x > k . Determine an expression for g-(x) , as well as its domain and range. (8 marks) Question 4 (a) Show that the following reduction formula holds, by using integration by parts: (cscx)" dx = - (csc x)"-2(cot x) + n - 2 n- 1 n (cscx)n-2 dx . (8 marks) (b) By repeated use of the reduction formula in Question 4(a), evaluate ( csc x ) 6 dx . (6 marks)