Prove that lim x f(x) = lim x0+ f(1/t) and lim x f(x) = lim x0- f(1/t)

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Prove that lim x→∞ f(x) = lim x→0+ f(1/t) and lim x→∞ f(x) = lim x→0- f(1/t) if these limits exist.
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