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Limit of a fraction

  1. Mar 21, 2008 #1
    Hi guys I have a question?

    lim x->1 (sqrt(x)-x^2)/(1-sqrt(x))

    What is the value of the limit of this function?

    Is it possible to be (-2)?????

    Or I AM WRONG?

    Thank you in advance.
  2. jcsd
  3. Mar 21, 2008 #2


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    … just divide …

    Hi nejnadusho! :smile:

    The bottom of this fraction actually factors the top, so you can just divide it out, if you want … :smile:
  4. Mar 21, 2008 #3

    I am sorry I cannot do it.

    I don't know how to do it
    Last edited: Mar 21, 2008
  5. Mar 22, 2008 #4

    Gib Z

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    It might help to let [itex] \sqrt{x} = u[/itex] so that it becomes

    [tex] \frac{u-u^4}{1-u} = \frac{ u(u^3-1)}{u-1}[/tex]

    Do you know how to factorize the u^3 -1 term?
  6. Mar 22, 2008 #5
    Thank you nOW I got it.

    No I don't know how to factorize this kind of terms
  7. Mar 22, 2008 #6
    [tex]a^3-b^3 = (a-b)(a^2+ab+b^2)[/tex]
    Can you proceed?
  8. Mar 24, 2008 #7
    Yes thanks
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