a) Prove that the function In(x + 1) is continuous at x = 0. You can use without proof that (In(x + 1))'= for x > -1. 2+1 b) Prove that there exists a point c (0, 1) such that 1 (7 marks) C 3. (In(4) - In(3)) You can only use without proof i) and ii) below. i) In(z) is differentiable for all r > 0. ii) Rolle's Theorem. (7 marks) c) State whether the following series converge or not. Justify your answer. n=1 n + n (n+1)2 ii) 1. n" + n