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Finding the value of a limit

  1. Jul 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the limit of x/(sqrt(1+3x)-1) as x approaches 0.

    2. Relevant equations
    The limit laws.

    3. The attempt at a solution
    I'm really stuck. I've tried multiplying all of it by (sqrt(1+3x)+1)/(sqrt(1+3x)+1), but that didn't work. I can't seem to get that 0 out of the denominator. What am I missing?
  2. jcsd
  3. Jul 6, 2012 #2
    What did you get after doing that multiplication?
  4. Jul 6, 2012 #3
    (x(sqrt(1+3x)+1))/3x. Or (x*sqrt(1+3x)+x)/3x if you will. But the 3x still goes to 0, so that doesn't seem to work.
  5. Jul 6, 2012 #4
    You can simplify it: you have x is numerator and denominator.
  6. Jul 6, 2012 #5
    Oh, wait! I realize what I did wrong. I'd seen that, yes, but made the stupid mistake of presuming that there would still be '2x' (instead of '3') left in the denominator. *slaps head* Thank you, micro. :smile:
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