(a) Using the formal definition of a limit, prove that f(x) = 2x-1 is continuous at the point x = 2; that is, lim-223-1 = 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 = 0; that is, limo cos(sin x)| = | cos(sin(x0))]. (c) Consider the irrational numbers 7 and 3/2. - (i) Prove that a common deviation bound of 0.00025 for both || and |y2| allows x + y to be accurate to + 2 by 3 decimal places. (ii) Draw a mapping diagram to illustrate your answer to (i).