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Math Help - Evaluating a limit to infinity

  1. #1
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    Evaluating a limit to infinity

    lim x/(sqrt(x^2+1000))
    x-> + inf

    the answer is not as important as its how its actually done. Thanks in advance.
    Last edited by simsima_1; November 11th 2007 at 05:42 PM.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by simsima_1 View Post
    lim x/(sqrt(x^2+1000))
    x-> + inf

    the answer is not as important as its how its actually done. I think L'Hopitals rule is used but i'm not so sure about the concept. Thanks in advance.
    ou can try L'Hopital's but i think it will be a pain here. (we can use L'Hopital's if when we take the limit our function goes to \frac 00 or \frac {\infty}{\infty})

    instead you should realize that as x \to \infty the + 1000 does not matter. thus

    \lim_{x \to \pm \infty} \frac x{\sqrt{x^2 + 1000}} = \lim_{x \to \pm \infty}\frac x{\sqrt{x^2}} = \lim_{x \to \pm \infty} \frac x{|x|} = \left \{ \begin{array}{lr} 1 & \mbox{ as } x \to \infty \\ -1 & \mbox{ as } x \to - \infty\end{array} \right.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by simsima_1 View Post
    lim x/(sqrt(x^2+1000))
    x-> + inf

    the answer is not as important as its how its actually done. Thanks in advance.
    Divide top and bottom by x to get:

    \lim_{x \to \infty} x/(\sqrt{x^2+1000})=\lim_{x \to \infty} \rm{sgn}(x)/(\sqrt{1+1000/x^2})=1

    RonL
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