2. (Statements about limits. ) Three statements are given below. Determine which statements are true and which are false. Prove the true statements, and disprove the false statements by giving examples with justification. (a) Let a E R. Suppose that f,g : R - R are two functions with the property that lim f(x), lim g(x) both do not exist. Then lim (f(r) + g(x) ) also does not exist. r-+0 (b) Suppose that f, g : R -> R both do not have any horizontal asymptotes. Then the product of f and g, denoted f . g, also does not have any horizontal asymptotes. (c) If f : R -> R, then there is at least one real number a E R such that lim f(r) exists