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Math Help - [SOLVED] limits

  1. #1
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    [SOLVED] limits

    lim(x→infinity) x^2sin(x) / 1-cosx

    how to show that limit is 0??

    attempt: i multiplied the bottom by 1+cosx
    but i dont know how to carry on. anybody can help me????many thanks
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  2. #2
    da`
    da` is offline
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    Is your question exactly show the lim (x-> infinity) f(x) = 0

    where f(x) =

    (x^2)Sinx
    1-Cosx

    ?
    ______

    as
    Sinx / (1-Cosx) = Cot (x/2) if that helps

    therefore (x^2)Cot (x/2)


    which leads me to believe that there doesnt exist a limit at all.

    I could be wrong.
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  3. #3
    MHF Contributor

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    Is your question f(x) = \frac{{x^2 \sin (x)}}{{1 - \cos (x)}}\,\& \,\lim _{x \to \infty } f(x) = ?.

    If so, then consider this: x_n  = \frac{\pi }{4} + 2n\pi  \Rightarrow \quad \lim _{n \to \infty } f(x_n ) = ?
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  4. #4
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    my mistake
    it is actually x tends to 0

    and i sorted out myself. thanks for those who paid attention
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