I have a problem figuring this out

  • Thread starter JasonRox
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  • #1
JasonRox
Homework Helper
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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.
 
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Answers and Replies

  • #2
uart
Science Advisor
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Yep, It's called using the first two terms of the binomial expansion and it comes in very handy. :)
 
  • #3
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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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