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Binomial Approximations

  1. Oct 18, 2005 #1
    Show that if x is small then

    1/(1+x) - root(1-2x) ~= (3/2)x^2


    im not sure how to even begin this question. there was a part 1 but i dont think its relevant. Small numbers just confuse me...how small is small in any case?
     
  2. jcsd
  3. Oct 18, 2005 #2

    HallsofIvy

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    You titled this "binomial Approximations"- obviously you are intended to expand both [itex]\frac{1}{1+x}= (1+x)^{-1}[/itex] and [itex]\sqrt{1- 2x}= (1-2x)^{\frac{1}{2}}[/itex] using the binomial formula. Then drop higher powers since if x is small, x to a power is much smaller.
    "how small is small in any case?" Well, in this case, small enough that the third power is negligible- because you were asked to show that this is approximately a number times x2
     
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