Q5. (9 marks) For the following series, find the radius of convergence R and the interval of convergence I. (3x - 2) (a) M ngn n=1 (b ) n=2 n! (In n)?' (c) E, n=1 Q6. (8 marks) In the following exercises, given that 1 - T Can with convergence in (-1, 1), n=0 find the power series for each function and identify its interval of convergence. 7: - 1 (a) f (x) = 3x2 + 2x - 1' Hint for (a): present the rational function in terms of partial functions. (b) f (x) = In (1+x) . Hint for (b): use term-by-term differentiation or integration to find power series for this function. Q7. (12 marks) In the following exercises, compute the Taylor or Maclauren series of each function around the given center a. (a) f (x) = sinx at a = = (b) f (x) = 27 at a = 0; (c) f(x) = 2 - 3x- + 1 at a = 1. Q8. (4 marks) Write the binomial series for the following function: f (x) = Vx + 8