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Math Help - Limits questions

  1. #1
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    Limits questions

    Some questions regarding limits:

    1- \lim(\sin(x) + x)/x
    x\rightarrow+\infty

    In this case, can I say that :
    1- \lim(\sin(x) ) /x  = 0 + 1 = 1 ?
    x\rightarrow+\infty

    I mean, I know that sin (x) when x approaches infinite does not exist, but since it will have a maximum range of 1~-1 I can say it is aproximadely 0?
    2- \lim(\cos(x) ) /(\frac{\pi}{2} - x)
    x\rightarrow\frac{\pi}{2}

    Here I dont have a single clue on how to do, seriously.

    Thanks in advance.
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  2. #2
    MHF Contributor matheagle's Avatar
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    1) is correct

    you can show that sin x divided by x goes to zero as x goes to infinity
    by the squeeze theorem

    {-1\over x}\le {\sin x\over x}\le {1\over x}

    2) can be done by L'Hopital's Rule. Have you seen that yet?
    Otherwise you can let u=pi/2-x and shift this.
    Last edited by matheagle; April 1st 2011 at 12:35 AM.
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  3. #3
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    Try L'Hospitals Rule for 2.
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  4. #4
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by Capes View Post
    2- \lim(\cos(x) ) /(\frac{\pi}{2} - x)
    x\rightarrow\frac{\pi}{2}
    The most secure way uses the basic trigonometric identity \cos x = \sin (\frac{\pi}{2} - x) that reports to the well known \displaystyle \lim_{\theta \rightarrow 0} \frac{\sin \theta}{\theta}...

    Kind regards

    \chi \sigma
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