- #1

- 9

- 0

## Homework Statement

Using the technique of Taylor expansion, find an approximate expression for the relativistic factor γ for small v (i.e., expanded around v = 0) that is correct to order v

^{2}.

## Homework Equations

γ=1/SQRT(1+ V

^{2}/C

^{2}). But in class, my professor just substituted X=V/C, so the equation became γ=1/SQRT(1-X

^{2}).

## The Attempt at a Solution

I tried to expand the function γ(v) with v at 0.....

γ(v)=1+γ'(0)(X-0)+(1/2)γ''(0)(X-0)

^{2}

However, this expression wasn't correct. I'm not really sure how else to expand it! Any help would be much, much appreciated, thanks!