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 [/(0), /(1)] UIf(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 lim, .. f(r) = 0? (A) We have lime-. f(x)g(x) = 0 since f(x)g(x) = 0 . g(x) =0. (B) We have lim, . f(x)g(r) = lim, .of(r) . lim, 9(r) = 0. (C) We have lime-wo f(r)g(x) # 0. (D) We cannot deduce any of the above. Q 3: An e - 6 proof We want to proof that lim 2r = 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 = 0/2. (B) For every o we can choose e = 26. (C) For every e we can choose & = 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, /(x) = -25 1-T-20 (A) y = 1. (B) y =0. (C) y = . (D) there is none. Q 5: Hyperbolic functions What is cosh r + sinh r? (A) exter. (B) e-. (C) 2ex. (D) ex