(a) If li'l' x} exists and lim g(x) does not exist, then lim (f(x)g(x)) does not exist. IH: IN'.' IH {b} It limx} exists and lim(f(x) g(x}) exists,

True or False? For each of the following statements, say if it is true or false. If it is true, give a proof.

If it is false, give a counterexample

(a) If li‘l'fl fix} exists and lim g(x) does not exist, then lim (f(x)g(x)) does not exist. I—H: I—N’.‘ I—Hfi {b} It limflx} exists and lim(f(x) — g(x}) exists, then lint g(x) exists. I—H.‘ I—HI I—J‘C {c} If “mffixl = m and fimsm = no: men fimUtx} —g(x)} = o I—HL‘ 3—H: 1—H? {d} If lim(f(x} +g(x) + h{x}) exists, then at least one of the limits lm1f(x},lri$g[x), limh(x) exists. 1—HT I—HC x—m (e) If f’(c] exists, then flu} exists.