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!

I have a problem figuring this out

  1. Aug 8, 2004 #1


    User Avatar
    Homework Helper
    Gold Member

    This is from Special Relativity, but it is not relevant to my question anyways.

    I am trying to simplify this:

    [tex]{\Delta}t = \frac{\ell}{c} \left[ \frac{1}{1- \beta^2} - \frac{1}{\sqrt{1 - \beta^2}} \right][/tex]

    - TO -

    [tex]{\Delta}t \approx \frac{\ell}{2c} \beta^2[/tex]

    For small x, [tex](1 + x)^n \approx 1 + n x[/tex]

    NOTE: Problem SOLVED. Feel free to try this out yourself. Make [tex]x = -\beta^2[/tex], it makes it easier, or I think it does.
    Last edited: Aug 8, 2004
  2. jcsd
  3. Aug 9, 2004 #2


    User Avatar
    Science Advisor

    Yep, It's called using the first two terms of the binomial expansion and it comes in very handy. :)
  4. Aug 9, 2004 #3
    One has to be careful , though approximations are common [edit]in[/edit]physics ... though it really demands sometimes to think how much approximate approximations should be :P

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook