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- Determine whether the following statement is true or false. If this statement is true, explain why. If this statement is false, provide a counterexample. If lim n→∞a_n = π, then a_n is divergent.Using the ε − N definition of a limit, prove that lim n→∞ (6n^3 −2n+1)/(2n^3 + 1) =3.Prove, using the formal definition, that limx→ 8 [(x)^1/3 = 2.]