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Math Help - limits

  1. #1
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    limits

    how can we evaluate


    limit [x sin (1/x)]
    x->0
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  2. #2
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    The sandwich theorem should work. Recall that \displaystyle -1 \leq \sin{\left(\frac{1}{x}\right)} \leq 1.

    This would mean
    \displaystyle \begin{align*} -x \leq x\sin{\left(\frac{1}{x}\right)} &\leq x \\ \lim_{x \to 0}(-x) \leq \lim_{x \to 0}{x\sin{\left(\frac{1}{x}\right)}} &\leq \lim_{x \to 0}x \end{align*}
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