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Math Help - Real Analysis - Functional Limits

  1. #1
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    Real Analysis - Functional Limits

    Let g: A --> R and assume that f is a bounded function on A, which is a subset of R (i.e. there exists M > 0 satisfying |f(x)| <= M for all x in A). Show that if lim as x-->c of g(x) = 0, then lim as x-->c of g(x)*f(x) = 0 as well.
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  2. #2
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    I had an idea using

    |f(x)g(x)|=|f(x)||g(x)| \leq M|g(x)|.

    Can we take the limit as x-> c of M|g(x)|?
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