- #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.

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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