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Math Help - Simply Convergence

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    Question Simply Convergence

    let $(f _n)_n \subset C^1((0,1), \Re)$ be a convergent sequence $ f (0,1) \rightarrow \Re $
    assume that $(f _n)_n \subset C^1 ((0,1), \Re) $ converges simply to $g=1$.
    Do we have $f \in C^1\left((0,1), \Re \right)$ ?
    Last edited by raheem; May 3rd 2014 at 07:24 AM.
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