# Determining asymptotic approach

1. Jul 19, 2005

### mmwave

I need to "determine the asymptotic approach of v to c, correct to powers of 1/t^2" in the equation below.

$$v = \frac{eEt/m_o}{\sqrt{1 + (eEt)^2/(m_oc)^2}}$$

Clearly the asymptote is c (speed of light) and I think I'm being asked to find an expression like constant * (1 + a1 / t + a2 / t^2 + ...) but I have not been able to do so. Power series don't work and binomial thm doesn't apply. Please help.

2. Jul 20, 2005

### arildno

$$v=\frac{c}{\sqrt{1+\epsilon}},\epsilon=\frac{(m_{0}c)^{2}}{(eEt)^{2}}$$
2. Make a power series expansion in $$\epsilon$$

3. Jul 21, 2005

### mmwave

Thanks Arildno. I guess I should have studied calculus in Norway.

Once I followed your advice I could also see that for any particle capable of reaching v approx. equal to c, I can use the binomial theorem.