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Limit prob

  1. Sep 12, 2013 #1
    1. The problem statement, all variables and given/known data
    lim x->1 (x^3-1)/(x^1/2-1)
    ans:6
    2. Relevant equations

    3. The attempt at a solution
    (x^1/2-1)^-1
    can be converted into (plugged into wolfram):
    (-x^1/2-1)/(1-x)
    i want to how this done if I'm factorize out the 0 in the denominator
     
  2. jcsd
  3. Sep 12, 2013 #2
    If I'm getting it right you have

    Numerator X³ -1
    Denominator Sqrt(x) - 1

    How can you factorize X³-1? If you know how the answer stares you right in the face.
     
  4. Sep 12, 2013 #3
    ok i may have expressed myself wrongly there.
    i wanted to know is how (1 / sqrt(x) - 1) can be converted into (-sqrt(x) - 1) / (1 - x)
    noticed it was just multiplying denominator and numerator by its conjugate.
    so yeah, should've noticed the elephant in the room.
    thanks for the help anyway.
     
  5. Sep 12, 2013 #4
    same way as 1/sqrt2 is sqrt2/2

    you lose square root in the denominator
    1*(sqrt(x) +1)/ (sqrt(x) -1)(sqrt(x) +1)
    sqrt(x) +1 / (x-1) , multiply both sides of the division sign by -1 and you arrive at what you are looking for.
     
  6. Sep 12, 2013 #5

    Ray Vickson

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    Science Advisor
    Homework Helper

    Why not let t = x^(1/2), and so have the limit of (t^6 - 1)/(t-1) as t → 1?
     
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