Alice, Bob, Charlotte, and Dan are thinking about limits, and they propose the following rules: 5 Alice: If lim f(x) = co and lim g(x) = co, then lim (f (x) + g(x) ) = 09. x-a x- a x-a Bob: If lim f(x) = co and lim g(x) = co, then lim (f (x) - g(x)) = 0. x-a x - a x- a f(x) * Charlotte: If lim f(x) = co and lim g(x) = co, then lim = 1. x-a x - a x-a g(x) Dan: If lim f(x) = co and lim g(x) = co, then lim f(x)g(x) = co. x-a x - a x-a Decide whether each rule is correct. If a rule is correct, explain why. If a rule is not correct, please give a counterexample (an example f(x) and g(x) for which the rule does not hold). Hint: Two of the rules are correct, and two are incorrect