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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’? ?x} exists and lim g(x) does not exist, then lim (f(x)g(x)) does not exist. I—H: I—N’.‘ I—H? {b} It lim?x} exists and lim(f(x) — g(x}) exists, then lint g(x) exists. I—H.‘ I—HI I—J‘C {c} If “mf?xl = m and ?msm = no: men ?mUtx} —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 ?u} exists.