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Binomial Theorem - small values of x and approximate values

  1. Oct 15, 2005 #1
    "Show that for small values of x, the function (1+x)^(-1/2) may be approximated by

    1-(1/2)x+(3/8)x^2

    Hence obtain the approximate value of 1/root(1.01) to 4 decimals."


    im totally clueless. the example we have isnt well explained at all. can someone even just start me off?


    (incidentally what happened to the flex pluggin? i went to find it for the maths bits but cant find it)
     
  2. jcsd
  3. Oct 15, 2005 #2

    Tide

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    Just replace x with 0.01 in your binomial expansion and you will have the desired approximation.
     
  4. Oct 15, 2005 #3
    what about the initial 'show that' bit?
     
  5. Oct 15, 2005 #4

    AKG

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    Do you know the binomial theorem?
     
  6. Oct 15, 2005 #5
    (a+b)^n = a^n +na^(n-1)b + (n(n-1))/2! (etc) ....that one?
     
  7. Oct 15, 2005 #6

    Integral

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    That's the one!

    Now you have 1.01 , think of it as a+b where a=1 and b=.01.

    Now, plug that into the binomial expansion, look at the magnitude of each monomial as you add them, continue until the terms are below your desired error.
     
  8. Oct 15, 2005 #7
    ok thanks for your help guys..just one more question..

    where did you get 1.01/0.01 from?
     
  9. Oct 16, 2005 #8

    HallsofIvy

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    ?? I don't see any reference to 1.01/0.01 in any of the previous responses!
     
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