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Math Help - showing that limit is zero

  1. #1
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    showing that limit is zero

    Hi there,

    how can I prove that lim x->0 sqrt(abs(x)).sin(1/x) = 0?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by dgmath View Post
    Hi there,

    how can I prove that lim x->0 sqrt(abs(x)).sin(1/x) = 0?
    Squeeze theorem.
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  3. #3
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    Quote Originally Posted by dgmath View Post
    Hi there,

    how can I prove that lim x->0 sqrt(abs(x)).sin(1/x) = 0?
    |\sqrt{|x|}sin\frac{1}{x}|\leq\sqrt{|x|}<\epsilon\  Longleftrightarrow|x|<\epsilon^2.

    So choose \delta<\epsilon^2
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  4. #4
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    squeeze theorem it is! thanks!
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