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 WITHOUT using l'hospital

  1. Jan 21, 2009 #1
    For [tex]p,q\in \mathbb{N}[/tex], determine [tex]\lim_{x\to1} \frac{x^{p}-1}{x^{q}-1}[/tex]

    I know that it should be p/q. Without using L'hospitals rule, how do I determine it?
  2. jcsd
  3. Jan 21, 2009 #2
    The quotient can be rewritten as (1-xp )/(1-xq ). Since x is less than 1 try a binomial expansion.
  4. Jan 21, 2009 #3
    Factoring :)
  5. Jan 21, 2009 #4
    Got it! My methods of trying were way more complicated. Don't know why I didn't think of that at first!

    (x^n) - 1=(x-1)(x^(n-1) + ... + x + 1)

    Thanks NoMoreExams
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook