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Determining asymptotic approach

  1. Jul 19, 2005 #1
    I need to "determine the asymptotic approach of v to c, correct to powers of 1/t^2" in the equation below.

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

    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. jcsd
  3. Jul 20, 2005 #2


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    1. Rewrite your expression as:
    2. Make a power series expansion in [tex]\epsilon[/tex]
  4. Jul 21, 2005 #3
    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.
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