[5, 2, 2, 4, 3 marks] (a) Using the formal definition of a limit, prove that f(x) = 2x³-1 is continuous at the point x = 2; that is, lim-2 2x³ - 1 = 15. (b) Let f and g be contraction functions with common domain R. Prove that (i) The composite function h := fog is also a contraction function: (ii) Using (i) prove that h(x) = cos(sin x) is continuous at every point x = xo; that is, limã→ro | cos(sin x)| = | cos(sin(xo))|. (c) Consider the irrational numbers and 2. (i) Prove that a common deviation bound of 0.00025 for both | - | and ly - 2 allows x + y to be accurate to π + √2 by 3 decimal places. (ii) Draw a mapping diagram to illustrate your answer to (i).'