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Math Help - sandwhich/squeeze theorm..help pls =]

  1. #1
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    sandwhich/squeeze theorm..help pls =]

    hi, im unsure on how to solve a certain limit using the sandwhich rule.

    lim [(x-3) sin(1/(3-x))] as x -> 3

    any help or hints would be much appreciated..thank you
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  2. #2
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    Quote Originally Posted by tasukete View Post
    hi, im unsure on how to solve a certain limit using the sandwhich rule.

    lim [(x-3) sin(1/(3-x))] as x -> 3

    any help or hints would be much appreciated..thank you
    The limit can be re-written as

    \lim_{y \rightarrow 0} (-y) \, \sin\left( \frac{1}{y} \right) = -\lim_{y \rightarrow 0}y \, \sin\left( \frac{1}{y} \right)

    where y = 3 - x.

    This in turn can be re-writen as - \lim_{t \rightarrow \infty} \frac{\sin t}{t}

    where t = \frac{1}{y}.

    Now read this.
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  3. #3
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    just need to confirm something....if y = x - 3

    wouldnt that make -y = 3-x ??? since u put:

    ysin(1/y) wouldnt it be: ysin(1/-y) instead? hope im right..
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  4. #4
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    oops :O pls ignore my previous post...read it in such a rush didnt see the -ve sign ...sry =] . thank you for your help so far
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