Approximate formula

  • Thread starter Yegor
  • Start date
  • #1
147
1

Main Question or Discussion Point

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
 

Answers and Replies

  • #2
185
3
have you tried arctan(1/x) for x->0?

and note:
arctan(1/x) = Pi/2 - arctan(x)
 
Last edited:
  • #3
147
1
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
 
  • #4
147
1
Great. i got next terms too. Thank you very much.
 

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