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Homework Help: Quick question on a limit

  1. Jul 13, 2010 #1
    I was copying some old text and I came across a limit I didn't understand.

    It starts as

    [tex]\stackrel{Lim}{x\rightarrow0}\frac{\sqrt{x^2+2-1}-x}{x}[/tex]

    and then understandably continues until


    [tex]\stackrel{Lim}{x\rightarrow0}\frac{x-1}{x*\sqrt{x^2+x-1}+x}=0[/tex]

    Why would this be zero? x-1 goes to -1, x goes to zero and anything multiplied by zero is zero. And dividing with zero is a no no...


    Sorry for the bad format I'm still trying to get a hang of latex.
     
    Last edited: Jul 13, 2010
  2. jcsd
  3. Jul 13, 2010 #2

    ehild

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    Homework Helper

    The second limit has no sense. The expression under the square root becomes negative when x--->0.

    ehild
     
  4. Jul 13, 2010 #3
    The second limit is derived from the first one. I know the second one makes no sense but its quite confidently written that it equals zero.

    Is the zero perhaps a reference to the first limit? And there was a mistake or typo made during solving?
     
  5. Jul 13, 2010 #4

    statdad

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    You must have made at least one transcription error.

    Your first expression

    [tex]
    \lim_{x \to 0} \frac{\sqrt{x^2+2-1}-x}{x}
    [/tex]

    does not exist - the expression goes to infinity IF what you have beneath the square root is correct.

    The second expression

    [tex]
    \lim_{x \to 0} \frac{x-1}{x\,\sqrt{x^2 + x -1} +x}
    [/tex]

    does not equal zero - it too goes to infinity (note that the denominator is

    [tex]
    x \left(\sqrt{x^2+x-1} + 1\right)
    [/tex]

    and this goes to zero as [itex] x [/itex] itself does. More importantly, this does not come from your first expression.

    Please examine your original problem and repost.

    I could attempt to "guess" different forms for the correct expression, but:
    - there is no guarentee would ever hit the correct one, even though I'm reasonably sure I would)
    - the weather is fantastic, my bicycle is ready to go, and there is a 55-mile ride mapped out that has my name on it. hoo-rah!
     
    Last edited: Jul 13, 2010
  6. Jul 13, 2010 #5
    Thanks for taking a look at this. I've found the same problem solved on some other notes I was doing and found the transcript error.
     
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