Q 1: Range of a continuous function Let f : [0, 1] U [2, 3] - R be a continuous function. What is the strongest statement we can make about the range of f? (A) The range is [f(0), f(3)]. (B) The range is an interval. (C) The range is [f(0), f(1)] U If(2), f(3)]. (D) The range is the union of two intervals. Q 2: Properties of the limit of a function Let f and g be two functions from Ry to R. What can we deduce from lime-to f (x) = 0? (A) We have lime-of (x)g(x) = 0 since f(x)g(x) =0 . g(x) = 0. (B) We have lime-of(x)g(x) = lime-of(x) . lime-+09(x) =0. (C) We have lime-of(x)g(x) # 0. D) We cannot deduce any of the above. Q 3: An e - d proof We want to proof that lim 2x = 6 using the e - o definition of continuity given in the lecture notes. Which of the following arguments is suitable?(A) For every o we can choose e = 6/2. (B) For every o we can choose e = 26. C) For every e we can choose o = c/2. (D) For every e we can choose o = 2c. Q 4: Asymptotes What is the horizontal asymptote of the following function? f : R \\ {-4,5} -R, f(x) = x2 - 25 12 - x - 20 (A) y = 1. (B) y =0. (C) y = F. (D) there is none. Q 5: Hyperbolic functions What is cosh a + sinha? ( A ) ete (B) e-z. (C) 27. (D) ex