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Math Help - Limit xsin(1/x), x->0

  1. #1
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    Limit xsin(1/x), x->0

    Hi
    Can anyone help me prove this?
    The limit of xsin(1/x) as x tends to 0 is 0.
    Ta very much
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    Re: Limit xsin(1/x), x->0

    Quote Originally Posted by liv205 View Post
    Hi
    Can anyone help me prove this?
    The limit of xsin(1/x) as x tends to 0 is 0.
    Ta very much
    I think it is more transparant to start by defining y = 1/x. Then your limit is of the form
    \lim_{y \to \infty} \frac{sin(y)}{y}

    Can you take it from here?

    -Dan
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