1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)
    2. Relevant equations

    3. The attempt at a solution
    can be converted into (plugged into wolfram):
    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

    User Avatar
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted