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I have a problem figuring this out

  1. Aug 8, 2004 #1

    JasonRox

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    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

    uart

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    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

    http://mathworld.wolfram.com/BernoulliInequality.html
     
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