3. [LATEX question] Given convergent sequences (an) and (bn) where lim ana, nx lim bnb, nx define the sequence (cn) by cn = max(an, bn) (where, just to be completely precise, we can define max(x, y) = = { xif xy, y otherwise. ). Show that lim cn = max(a, b). (Hint: consider the cases a = b, a ‡ b) n x

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