1. Not finding help here? Sign up for a free 30min 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!

Problem using L'Hospiital's Rule (indeterminate form: INF - INF)

  1. Sep 19, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\stackrel{lim}{x\rightarrow\infty}(\sqrt{x^2+x} - x)[/tex]

    I have no idea how to do this. In my book, it says I want to convert [tex]\infty - \infty[/tex] forms into a quotient by getting a common denominator, rationalization or by factoring.
     
  2. jcsd
  3. Sep 19, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I would say you want to multiply by (sqrt(x^2+x)+x)/(sqrt(x^2+x)+x). I.e. rationalize.
     
  4. Sep 19, 2009 #3

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Many, many things would work, really. Multiplying and dividing by 1/x, for example.

    Why 1/x? Well, it might be more clear if you think of it as "factoring out an x" -- then you just move the x to be a 1/x in the denominator so that you can use L'hôpitals.
     
  5. Sep 19, 2009 #4
    how about doing this :

    y = sqrt(x^2 + x) - x

    = sqrt(x ( x + 1) ) - x

    = sqrt(x) * sqrt(x+1) - x

    The use the product rule for term 1, combined with chain rule.

    or
    y = sqrt(x^2 + x) - x

    = 1/x(sqrt(x^2 + x) - x)
    = 1/x *sqrt(x^2 + x) - 1
    = sqrt( (1/x)^2 ) * sqrt ( x^2 + x) - 1
    = sqrt( (1/x)^2 ( x^2 + x) ) - 1
    = sqrt( 1 + 1/x ) - 1

    the use l'hopital rule.
     
  6. Sep 19, 2009 #5
    ^do that

    [tex] (\sqrt{x^2+x}-x).\frac{(\sqrt{x^2+x}+x)}{(\sqrt{x^2+x}+x)} = \frac{1}{\frac{x}{x}\sqrt{1+\frac{1}{x^2}}+1} [/tex]
     
    Last edited: Sep 19, 2009
  7. Sep 19, 2009 #6
    I tried out all your suggestions. This is really cool. Thx everyone.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem using L'Hospiital's Rule (indeterminate form: INF - INF)
Loading...