# Taylor series question

• March 23rd 2014, 07:20 PM
Anewk
Taylor series question
How would I find the second-degree Taylor series for $x^2+y^2=4$ at $[1, -\sqrt[]{3}]$?
• March 23rd 2014, 08:24 PM
romsek
Re: Taylor series question
Quote:

Originally Posted by Anewk
How would I find the second-degree Taylor series for $x^2+y^2=4$ at $[1, -\sqrt[]{3}]$?

note that given the point they want you to expand about, $(1,-\sqrt{3})$ you can write

$y(x)=-\sqrt{4-x^2}$

and just take the first couple of derivatives and evaluate at $x=1$ and plug into your taylor series formula.