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!

Can't find limit

  1. Sep 15, 2009 #1


    User Avatar
    Gold Member

    Find the limit.

    \lim_{x \rightarrow 0} \frac{\frac{1}{x + 1} - 1}{x}

    My attempt
    I'm totally stuck. domain(f) = R - {0}. Setting g: R - {-1} --> R, g(x) = 1/(x+1) - 1 and h: R --> R, h(x) = x, g and h are both continuous, but g(0) = 0 and h(0) = 0. It looks like f(0) is just a hole. Perhaps I will try factoring again. My book says the limit is -1, but I don't see how it expects me to find it.
  2. jcsd
  3. Sep 15, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Hi honestrosewater! :smile:

    erm :redface:

    what's 1/(x+1) - 1 ? :wink:

    ( alternatively, use l'Hôpital's rule )
  4. Sep 15, 2009 #3


    User Avatar
    Gold Member

    1/(x + 1) - 1 = -x/(x+1)? Does that help me somehow? Sorry, I am sure it's something simple, but I cannot see it. Oh... right.

    [tex]\left(\frac{-x}{x + 1}\right)\left(\frac{1}{x}\right) = \frac{-1}{x + 1} = g(x)

    g is continuous and x != 0 implies g(x) = f(x), so lim(x --> 0) f(0) = lim(x --> 0) g(0) = -1. Hah.

    Thanks for this tip. I will remember it later. Unfortunately, passing my test means applying the algorithms that the book has taught us, and we have not covered derivatives yet or been taught that rule. I have already been warned about using theorems that I am not supposed to know.

    Thanks! :^)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook