2) Let f(x) = . 27. have a removable discontinuity? a) f has a removable discontinuity at x = 1 and an essential discontinuity at x = 0. b) f has a removable discontinuity at x = 0 and an essential discontinuity at x = 1. c) f has a removable discontinuity at both x = 0 and x = 1. d) f has an essential discontinuity at both x = 0 and x = 1. e) f is continuous at x = 0. 5) Together the IVT and the EVT show that a) if f(x) is continuous on (a, b), then f((a, b)) is an open interval. b) if f(x) is continuous on [a, b], then f([a, b]) is a closed interval. c) if f(x) is continuous on (a, b], then f((a, b]) is a half open interval. d) All of the above. 6) The polynomial p(x) = x tax? +br +c has all integer roots and has the following additional property: T-value x = -3.4 x = -2.2 x = -1.5 x = -0.1 x =0.7 x =1.4 x=2.8 x= 3.5 sign of P(I) + + + + Which of the following statements is always true? a) p(-2) = 0 b) p(2) > 0 c) a =1 d) All of the above. 7) Assume that p(I) is a polynomial of odd degree. In particular, p(x) = do + a,I + a2x2 + . . . + and where n is odd. Then it can be shown that p(x) must have at least one real root. Which of the following results can be used to justify this statement? a) Extreme Value Theorem b) Intermediate Value Theorem c) The Sequential Characterization of Limits d) None of the above