True or False: If the statement is true, explain or prove why. If the statement is false, give a counterexample that disproves the statement. (a) If lim f (x) = 0 and lim g(x) = 0 then lim / (2) does not exist. x-2 x-2 x-29(x) (b) There exists a function f(x) such that lim f(x) = 2. x-1 (c) The function f(x) = x3 - ex has a zero in the interval (1,2). (d) If lim f (x) = 0 then lim xf (x) = 0. X +00 X+00