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Thread: use squeeze theorem to

  1. #1
    Member sluggerbroth's Avatar
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    Post use squeeze theorem to

    use squeeze theorem to establish limit

    lim (as x goes to zero) of x sin(1/x)=0




    also help with keying problem? symbosl etc?
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    Re: use squeeze theorem to

    For all $\displaystyle x \in \Re $,
    $\displaystyle -1 \leq sin(x) \leq 1 $.

    This is also valid for $\displaystyle 1/x \in \Re$ $\displaystyle x \neq 0$,
    $\displaystyle -1 \leq sin(1/x) \leq 1 $.

    Multiply by $\displaystyle x $ and apply the squeeze theorem.

    Examples of using Latex (the symbols) can be found here Use [tex] and [/tex] tags NOT [math] and [/math] tags for latex. and LaTex Tutorial
    Last edited by Krahl; Jun 7th 2012 at 07:21 AM. Reason: changed from 0 < sin(x) < 1
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    MHF Contributor Reckoner's Avatar
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    Re: use squeeze theorem to

    Quote Originally Posted by Krahl View Post
    For all $\displaystyle x \in \Re $,
    $\displaystyle 0 \leq sin(x) \leq 1 $.
    I think you mean, for all $\displaystyle x$, $\displaystyle -1\leq\sin x\leq1$.
    Thanks from Krahl
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    Re: use squeeze theorem to

    Quote Originally Posted by sluggerbroth View Post
    use squeeze theorem to establish limit
    lim (as x goes to zero) of x sin(1/x)=0
    also help with keying problem? symbosl etc?
    Learn LaTeX coding.
    [TEX]{\lim _{x \to 0}}x\sin \left( {\frac{1}{x}} \right)[/TEX] gives $\displaystyle {\lim _{x \to 0}}x\sin \left( {\frac{1}{x}} \right)$.
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    Re: use squeeze theorem to

    Quote Originally Posted by Reckoner View Post
    I think you mean, for all $\displaystyle x$, $\displaystyle -1\leq\sin x\leq1$.
    Sorry, yes that's the one.
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