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Lim sqrt(x)/sqrt(10x+1) ?

  1. Dec 15, 2009 #1
    lim sqrt(x)/sqrt(10x+1) ??

    Limit as x tends to infinity of sqrt(x)/sqrt(10x+1) = sqrt(1/10), but how?

    I'm trying to understand this, so, it's the sqrt[x/(10x+1)], but how do i simplify that to make it a limit i can set to infinity. I know the problem isn't my calculus skills, but my algebra skills!
     
  2. jcsd
  3. Dec 15, 2009 #2

    Mark44

    Staff: Mentor

    Re: lim sqrt(x)/sqrt(10x+1) ??

    Factor x out of both terms in the denominator.
    [tex]\frac{x}{10x + 1}~=~\frac{x}{x(10 + 1/x)}[/tex]

    Now, what's the limit of the latter expression as x gets large?
     
  4. Dec 15, 2009 #3
    Re: lim sqrt(x)/sqrt(10x+1) ??

    If we set x to infinity we get infinity/infinity(10) which is just equal to infinity/infinity?? The limit as x gets very large is 1 though.

    Why did you take off the radical sign, btw, is that part of simplification?
     
  5. Dec 15, 2009 #4
    Re: lim sqrt(x)/sqrt(10x+1) ??

    nevermind, i got it. thanks a lot.
     
  6. Dec 15, 2009 #5

    Mark44

    Staff: Mentor

    Re: lim sqrt(x)/sqrt(10x+1) ??

    infinity/infinity or infinity - infinity is NEVER the answer.

    I was working inside the radical...
     
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