Problem 3 (3 marks). Using the E, 8 definition of continuity, show that the following functions are continuous on R. Since the problem is worth only 3 marks, you can restrict your answer to three of the options below. (a) f(x) = x; ( b ) 8 (x ) = x2; (c) h(x) = x3; (d) 4(x) = x, for all n E N. Hint: One strategy for this question is to use the identity in Equation 1 to show part (d), and the rest will follow immediately by letting n be equal to 1,2, and 3, respectively. But try to solve parts (b) and (c) first, to get intuition for (d). The key observation is that if x and y are sufficiently close to each other, then the summation that appears in the right-hand side of Equation 1 is bounded. 1 Recall that x > y holds whenever x; > y; for all i = 1, ..., n