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Approximate formula

  1. Jul 4, 2005 #1
    There exist such a formula for large x:
    [tex]\arctan(x)\approx \pi/2-1/x+1/3x^3...[/tex]
    I can't understand how it is derived. I tried to get it from Taylor series (for x -> infinity) and understood that here is something different. Can someone help me?
    Thank you
     
  2. jcsd
  3. Jul 4, 2005 #2
    have you tried arctan(1/x) for x->0?

    and note:
    arctan(1/x) = Pi/2 - arctan(x)
     
    Last edited: Jul 4, 2005
  4. Jul 4, 2005 #3
    Hm. This is what i got:
    [tex] f(x)=\arctan(1/x);
    f'(x)=-\frac{1}{1+x^2};
    f(x)\approx f(0)+f'(0)(x-0)=\pi/2-x[/tex]
    yes. it looks good
     
  5. Jul 4, 2005 #4
    Great. i got next terms too. Thank you very much.
     
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