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: Oblique asymptote question

  1. Apr 25, 2008 #1
    I am trying to draw the graph of

    y = x + \sqrt{|x|}

    Can I say that as x approaches infinity, y approaches x? That would mean that the function has an oblique asymptote at the line y=x but I'm not sure.

    Thanks for any help!
  2. jcsd
  3. Apr 25, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    y=x is an asymptote if (and only if):
    y-x approaches zero as x approaches infinity.

    Try subtracting x from both sides of your equation, and see whether the right-hand-side expression approaches zero or not.

    Alternatively, you could plug in successively larger values of x into your expression (i.e, 100, then 1000, then 10,000).
    Does the difference between the value and the value of x get larger or smaller?

    Eg., for x = 100:
    100 + sqrt(100) = ?
    This number is ____ larger than 100.
    Repeat for 1000, then 10,000.
  4. Apr 25, 2008 #3
    Thanks for the reply. Thats what I was thinking, the difference gets larger as x gets larger. But then I thought, when you have a function like x^2 + x, it behaves more and more like x^2 as x gets larger. This function behaves more like x as x gets larger, doesn't it?
  5. Apr 25, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Both statements are true, these functions "behave more like" x^2 and x, respectively. However, to be an asymptote is a more stringent requirement.

    It's likely that, if encountered in a physics or engineering application, you'd be completely justified in approximating the function simply by y=x for large x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook