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Approximating an expression with the binomial expansion

  1. Sep 24, 2006 #1
    [tex]f_r=(\frac{1+v}{1-v})f_i[/tex]

    For an automobile moving at speed v that is a small fraction of the speed of light, assume that the fractional change in frequency of reflected radar is small. Under this assumption, use the first two terms of the bionomial expansion

    [tex](1-x)^n\approx{1-nz \mbox{for} |z| \ll{1}[/tex]

    to show that the fractional change of frequency is given by the approximate expression

    [tex]\frac{\Delta{f}}{f}\approx{2v}[/tex]



    So far, I have

    \frac{\Delta{f}}{f}=\frac{\frac{1+v}{1-v}\Delta{f_i}}{\frac{1+v}{1-v}f_i

    Now, does the binomial expansion allow this?: [tex]\frac{1+v}{1-v}\approx{(1+v)(1+v)}[/tex]

    Is this where this problem wants me to go?
     
    Last edited: Sep 24, 2006
  2. jcsd
  3. Sep 24, 2006 #2
    Can someone also please show me the errors in my two non-latex equations? They don't seem to want to play nicely.:cry:
     
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