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: Difference of Squares?

  1. Apr 21, 2007 #1
    I'm reviewing material for my exams and I came across this:

    [tex]\lim _{x\rightarrow \infty }\sqrt {{x}^{2}+x+1}-\sqrt {{x}^{2}-3\,x}[/tex]

    The only explanation it gives is "By the difference of squares" the solution sheet then jumps to:

    [tex]\lim _{x\rightarrow \infty }{\frac {4\,x+1}{\sqrt {{x}^{2}+x+1}+\sqrt

    What the hell just happened there? I can solve from then on but I've no idea what's happening on this step. Also an idiot proof link would be appreciated.
  2. jcsd
  3. Apr 21, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Think of the first line as [tex]\lim _{x\rightarrow \infty }\frac{\sqrt {{x}^{2}+x+1}-\sqrt {{x}^{2}-3\,x}}{1}[/tex], then multiply top and bottom of the fraction by [itex]\sqrt {{x}^{2}+x+1}+\sqrt {{x}^{2}-3\,x}[/itex]. Does this make the second line any clearer?
  4. Apr 21, 2007 #3
    *Hits head on wall*
    Yes, thanks.
  5. Apr 21, 2007 #4


    User Avatar
    Homework Helper
    Education Advisor
    Gold Member

    I just tried it myself; how does "2" seem?
  6. Apr 21, 2007 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    2 sounds good, since the function looks like
    [tex]\frac{4x}{\sqrt{x^2} + \sqrt{x^2}} = 2[/tex]
    when x is big.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook