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Limit as x tends to 1

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data

    evaluate limit as x tends to 1:


    2. Relevant equations

    3. The attempt at a solution

    =lim (x^(1/3)-1)^2/(x-1)^2

    what do i do next??
    (note, i dont want to use l'hospitals rule)
  2. jcsd
  3. Nov 30, 2008 #2
    ......hmmm..... why not?

    Attached is my solution.

    Attached Files:

    Last edited: Nov 30, 2008
  4. Nov 30, 2008 #3


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    Substitute y = x1/3 Then

    [tex] \frac{(x^{1/3}-1)^2}{(x-1)^2} = \frac{(y-1)^2}{(y^3-1)^2} [/tex]

    and y3-1 = (y-1)(y2 + y + 1)
  5. Nov 30, 2008 #4
    I can't believe that. I worked it out straight away but it took me like 30 mins to make that PDF lol.... i wish i'd known this forum had LaTeX... then I might not have used LyX :smile:

    Nike: Every day is a competition.
  6. Nov 30, 2008 #5
    Thank you very much wimma and office shredder.
  7. Nov 30, 2008 #6
    no problem XD
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