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Math Help - Riemann integrable, bounded

  1. #1
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    Riemann integrable, bounded

    Suppose that f: [a,b] \rightarrow \mathbb{R} is Riemann integrable on [a,b] and \frac{1}{f} is bounded on [a,b]. Prove that \frac{1}{f} is Riemann integrable on [a,b].
    Relevant Theorems/Definitions
    Definition - Riemann integrable - if upper integral of f(x)dx= lower integral of f(x)dx.
    Theorem - Riemann integrable iff for each \epsilon > 0 \exists a partition P of [a,b] such that U(P,f)-L(P,f) \leq \epsilon.
    Theorem - Riemann integrable iff \exists A \in \mathbb{R} such that \forall \epsilon >0 \exists a partition P of [a,b] such that \forall marked refinements Q of P, |S(Q, f) - A | \leq \epsilon, where A=\int^a_b f(x)dx.
    Theorem - Let f: [a,b] \rightarrow \mathbb{R} be a continuous function on [a,b]. Then f is Riemann integrable on [a,b].
    etc.

    I don't know how to start this problem. I need a head start on where to go with this one. Thanks in advance.
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  2. #2
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