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Math Help - Trig Limit

  1. #1
    Member akhayoon's Avatar
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    Trig Limit

     \lim_{x\to1^{-1}}(x-1) sin(\frac{1}{x-1})

    I heard that the answer equals 0, if so how is this?

    thank you
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  2. #2
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    Let t=x-1 to get \lim_{t\to 0}t\sin \frac{1}{t}.

    Note, \left| \sin \frac{1}{t}\right|\leq 1 use squeeze theorem.
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