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Without using L'Hopital's rule, how can I calaculate this limit?

  1. Jan 18, 2013 #1
    Without using L'Hopital's rule how can I calculate the limit of this function: (xn-an)/(x-a) when x→a

    I cannot get rid of the indeterminations no matter what. I would like if you could help me out on this.
  2. jcsd
  3. Jan 18, 2013 #2


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    Factor x^n-a^n. For example x^2-a^2=(x-a)(x+a). x^3-a^3=(x-a)(x^2+xa+a^2) etc.
  4. Jan 18, 2013 #3

    Ray Vickson

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    Is n a positive integer? If so, just factor, as Dick has already suggested. If n is not a positive integer, you more-or-less need to use l'Hosptial's rule, whether you want to or not.
  5. Jan 18, 2013 #4
    I figured that out. Took me a while to notice if I factorized x^n-a^n begining with (x-a)(...) the sum of the other factors would add up to n.a^n-1.

    PS: I apologize not having posted my original atempt in solving the problem like the rules require.
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