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(a) Prove that the following result is true for all real numbers x: if x 0 and x (a) Prove that the following result is

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(a) Prove that the following result is true for all real numbers x: if x 0 and x

(a) Prove that the following result is true for all real numbers x: if < 1, then lx lx . (Hint: Consider separately the cases x = O, x > O and x < O). (b) Hence or otherwise, use the precise definition of a limit to prove that lim x3 0.

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