(c) What is lim f[g(x)]? Explain your reasoning. X- 00 O Since the limit as x approaches infinity of g(x) is equal to infinity and the limit as x approaches infinity of f(x) is equal to -1, then the limit as x approaches infinity of fly(x)] is equal to infinity. Since the limit as x approaches infinity of f(x) is equal to infinity and the limit as x approaches infinity of g(x) is equal to -1, then the limit as x approaches infinity of fly(x)] is equal to -1. O Since the limit as x approaches infinity of g(x) is equal to infinity and the limit as x approaches infinity of f(x) is equal to -1, then the limit as x approaches infinity of fly(x)] is equal to -1. O Since the limit as x approaches infinity of f(x) is equal to infinity and the limit as x approaches infinity of g(x) is equal to -1, then the limit as x approaches infinity of fly(x)] is equal to infinity. (d) If h ( x) = [f(x) + g(x), -2 5 x 5 0 what is k so that h(x) is continuous at x = 0? k + g(x)f (x ), x >0, K =Use the graphs of f(x) and g(x) given below to answer the following questions. f(x) g(x) 2 (0, 2) 20 1 (0, 1) 19 (-2,0) (0,0) X -4 -2 2 4 -4 -2 2 4 - 10 -1 (-2, -1) -3 -3 (a) Is f[g(x)] continuous at x = 0? Explain why or why not. O Yes, f[g(x)] is continuous at x = 0 since the limit as x approaches 0 of f[g(x)] = fig(0)] = -1. O Yes, f[g(x)] is continuous at x = 0 since the limit as x approaches 0 of f[g(x)] = fig(0)] = 0. O No, fig(x)] is not continuous at x = 0 since the limit as x approaches 0 of fly(x)] = flg(0)] = -1. O No, fig(x)] is not continuous at x = 0 since the limit as x approaches 0 of f[g(x)] does not exist since the limits from the left and right are not the same. (b) Is g[f(x)] continuous at x = 0? Explain why or why not. O Yes, g [f(x)] is continuous at x = 0 since the limit as x approaches 0 of g [f(x)] = g [f(0)] = 0. O Yes, g [f(x)] is continuous at x = 0 since the limit as x approaches 0 of g [f(x)] = g [f(0)] = 2. O No, g [f(x)] is not continuous at x = 0 since the limit as x approaches 0 of g [f(x)] = g [f(0)] = 2. O No, g [f(x)] is not continuous at x = 0 since the limit as x approaches 0 of g [f(x)] does not exist since the limits from the left and right are not the same