Problem with Lagrangian function

[Mateusz]

Hello,
I trying to understood some transition from one equation to another but i need a little help with that.
So we have, a

Had problems with Latex :).

 

[Geofleur]

Use a Taylor expansion, $f(x+\Delta x) \approx f(x) + \frac{df}{dx}\Delta x$ with $f = L$, $x = v^2$, and $\Delta x = 2v\epsilon$.

 

[Mateusz]

Ohh so when he said "powers series" he means "Taylor expansion", thank you :)