Approximation Definition and 705 Threads

I am a bit confused about taylor approximation. Taylor around x_0 yields f(x) = f(x_0) + f'(x_0)(x-x_0) + O(x^2) which is the tangent of f in x_0, where f'(x) = f'(x_0) + f''(x_0)(x-x_0) + O(x^2) which adds up to f(x) &=& f(x_0) + (f'(x_0) + f''(x_0)(x-x_0) +...

I'm doing a problem on Van-der Walls interaction and was told in the hint of the problem to use the approximation kT>>hw to simplify {-hw/(2kT)}-Ln[Exp[-hw/(kT)]-1] I have no idea how to apply this approximation to simpify the problem. Thanks

Does anyone know the basics of the local spin density approximation?

http://www.geocities.com/dr_physica/moa.zip is a delphi program showing how my method of approxim outperforms/beats the Newton's one while looking for sqrt(2) try the case A+B=2*sqrt(2) and see the magic!

I was wondering how Stirling's approximation x! ~ sqrt(2[pi]x)xxe-x was derived. Anyone know?