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Homework Help: Limit calculation

  1. Sep 20, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the limit [tex]\lim\limits_{t\to -1}\frac{\sqrt[3]{t}+1}{\sqrt[5]{t}+1}[/tex]. Needless to say: No L'Hopital's rule, otherwise this thread would not exist.

    2. Relevant equations

    3. The attempt at a solution
    Have tried multiplying the fraction such that I get the difference of squares in denominator - no avail.
    This is analysis 1 course material .. *blushes*

    There is something I have forgotten about, this is supposed to be a really easy problem.
    Hints, anyone?
  2. jcsd
  3. Sep 20, 2015 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Did somebody forbid you from using l'Hospital's rule?
  4. Sep 20, 2015 #3


    Staff: Mentor

    Of course that won't work -- neither radical contains a square root.

    What will work is to multiply each of the numerator and denominator by 1, in a suitable form.

    Hint 1: ##(a + b)(a^2 - ab + b^2) = a^3 + b^3##
    Hint 2: ##(a + b)(a^4 -a^3b + a^2b^2 - ab^3 + b^4) = a^5 + b^5##
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