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5. Let {an1 be a sequence. (a) Prove that limnan = L if and only if limno (an - L) = 0. (b) Prove that limn→∞ an = 0 if and only if limn→∞ |an| = 0. (c) Prove that if limn→∞ an = L, then limn→∞ |an| = |L|.