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Let \(f : \mathbb{R} \to \mathbb{R}\) such that for every non-zero \(h\) in a neighborhood of \(0\), $$ f(h) = 3 + 2 h + h^2 \cos(1/h), $$ and \(f(0) = 3\). Show, by direct application of the \(DL_1\) characterization, that \(f\) is differentiable at \(0\) and compute \(f'(0)\).
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