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Approximation involving an exponential function

  1. Jul 26, 2011 #1
    1. The problem statement, all variables and given/known data

    I was following a derivation of some laws and I didn't get how they approximate some portion of the expression. That portion/part is exp[gbH/(2kT)]. The book says gbH/2 <<1 and therefore exp[gbH/(2kT)] = 1+gbH/(2kT).
    2. Relevant equations



    3. The attempt at a solution
    I agree with the value 1, but where did gbH/(2kT) come from? Please help. My understanding is that if gbH/2 is way less than 1, then e.g exp[1.0*10^-15/KT)] = 1.
     
  2. jcsd
  3. Jul 26, 2011 #2
    Because it's the Taylor expansion of exp(x) near 0

    exp(x) = 1 + x + (x^2)/2 + (x^3)/6 + ...

    You can cut the series at any term you would like, however you can't equal it to 1 because there will be no parameter left to give values to...
     
  4. Jul 26, 2011 #3

    HallsofIvy

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    You can also get this approximation by replacing the curving graph by a tangent line.
     
  5. Jul 27, 2011 #4
    Haa, thank you very much. That didn't pop in my head. Thanks a lot.
     
  6. Jul 27, 2011 #5
    Thanks for that.
     
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