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Let \(f : \mathbb{R} \to \mathbb{R}\) such that \(\lim_{x \to 0^+} f(x) = 1\), \(\lim_{x \to 0^-} f(x) = 1\), and \(f(0) = 1\). Show that \(\lim_{x \to 0} f(x) = 1\).
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