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Math Help - real analysis

  1. #1
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    real analysis

    Suppose f is infinitely differentiable on \mathbb{R}.

    (a) If \left|{f(x)\right|\leq 1 + \left|x\right|^m for some m\in \mathbb {N}, and for all x\in\mathbb{R},then f(x) is a polynomial.
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  2. #2
    Junior Member
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    Apr 2010
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    This is not true: take f(x)=\sin(x) and note the statement is true for any m\in\mathbb{N}.
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