(a) In this part of the question, you may assume any results that are proved in Unit F1, but you should refer to any results that you use. Prove each of the following statements. 2+2+ 2 (i) lim x--1x2 - 2x - 3 x3 - 4 log x (ii) lim = 0 4x + 3ex (b) Prove that the function f (a) = sin does not tend to a limit as x tends to 0. (c) Use the E-6 definition of continuity to prove that the function f (z) = 2x2 + x is continuous at c = -1. (d) Prove that the function f (2 ) = 3 x + 1 is uniformly continuous on the interval [0, 2], referring to any results from the module that you use