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!

Limit x->-infinity (x/(z^2+x^2)^0.5) = ?

  1. Jun 22, 2005 #1

    Eus

    User Avatar

    Hi Ho! :smile:

    Mmmm... I have a problem with this one:

    [itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}}[/itex]

    Using a computer graphics tool, I found that the result should be -1 by looking at the generated graph.

    But if I do it by hands, I find 1 as follows:

    [itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}} = \lim_{x\rightarrow-\infty} \frac{x \frac{1}{x}}{\sqrt{z^2+x^2} \frac{1}{x}}[/itex]
    [itex]= \lim_{x\rightarrow-\infty} \frac{1}{\sqrt{\frac{z^2+x^2}{x^2}}}[/itex]
    [itex]= \lim_{x\rightarrow-\infty} \frac{1}{\sqrt{1+(\frac{z}{x})^2}}[/itex]
    [itex]= \frac{1}{\sqrt{1+(\frac{z}{-\infty})^2}}[/itex]
    [itex]= \frac{1}{\sqrt{1+0}}[/itex]
    [itex]= \frac{1}{1}[/itex]
    [itex]= 1[/itex]

    Would you please correct my mistake?

    Thank you very much! :biggrin:
     
    Last edited: Jun 22, 2005
  2. jcsd
  3. Jun 22, 2005 #2
    hello there

    check this out

    [itex]\lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}}[/itex]
    [itex]=\lim_{n\rightarrow\infty} \frac{-n}{\sqrt{k^2+n^2}}[/itex]
    [itex]= \lim_{n\rightarrow\infty} \frac{-n\frac{1}{n}}{\sqrt{k^2+n^2} \frac{1}{n}}[/itex]
    [itex]= \lim_{n\rightarrow\infty} \frac{-1}{\sqrt{\frac{k^2+n^2}{n^2}}}[/itex]
    [itex]= \lim_{n\rightarrow\infty} \frac{-1}{\sqrt{1+(\frac{k}{n})^2}}[/itex]
    [itex]= \frac{-1}{\sqrt{1+0}}=-1[/itex]

    always try to simplify it to something that looks simple

    take care

    steven
     
  4. Jun 22, 2005 #3

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    I hope you saw your mistake,you shouln't have sent "x" into its square when taking the limit to "-infinity".

    Daniel.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Limit x->-infinity (x/(z^2+x^2)^0.5) = ?
Loading...