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!

Limit as x tends to infinity, without Laurent

  1. Jan 31, 2015 #1
    1. The problem statement, all variables and given/known data
    I want to find the following limit, ## \lim_{x \rightarrow \infty } x( \sqrt{ x^{2} +9} -x) ##, without using the Laurent series
    2. Relevant equations
    None.

    3. The attempt at a solution
    I used the Laurent Series to expand the square root, giving ## x((x+\frac{9}{2x})-x)##, then giving the limit as ##\frac{9}{2}## . How would one go about this question without using the above method?
     
  2. jcsd
  3. Jan 31, 2015 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    ... to me that reads:$$\lim_{x\to\infty}x\sqrt{x^2-x+9}$$ ... I don't think that converges: perhaps you meant to write something different.

    Mostly someone would deal with a limit like that by remembering how the functions work for the limit in question.
    i.e. as x gets very big, large powers of x will come to dominate a sum.

    So: $$\lim_{x\to\infty} \frac{x}{\sqrt{x^4-2x+9000}}=\lim_{x\to\infty}\frac{1}{x} = 0$$ ... which you can check on a calculator.

    I find it suggestive that the 9 under the root is a square number - so if you want to be more rigorous-ish, try completing the square, look for a substitution maybe?
     
    Last edited: Jan 31, 2015
  4. Jan 31, 2015 #3

    Mark44

    Staff: Mentor

    The OP has something different. I don't believe it was edited, but perhaps it was.

    @Skeptic, multiply by ##\sqrt{x^2 + 9} + x## over itself, and you'll be able to take the limit.
     
  5. Jan 31, 2015 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Oh I see - my display is not showing the line over the square-root in post #1, and it didn't drag to quote in my reply either - but I do see it quoted in post #3.
    Cheers.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Limit as x tends to infinity, without Laurent
Loading...