- #1

Yegor

- 147

- 1

[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

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- Thread starter Yegor
- Start date

- #1

Yegor

- 147

- 1

[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

qbert

- 185

- 5

have you tried arctan(1/x) for x->0?

and note:

arctan(1/x) = Pi/2 - arctan(x)

and note:

arctan(1/x) = Pi/2 - arctan(x)

Last edited:

- #3

Yegor

- 147

- 1

[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

Yegor

- 147

- 1

Great. i got next terms too. Thank you very much.

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