# taylor polynomial help!

• Oct 21st 2011, 01:04 PM
Kuma
taylor polynomial help!
I don't really understand how to derive taylor polymomials for questions like these for example

find the 3rd degree taylor polymomial about the origin of
f(x,y) = (cos y) ln(xy+1)

• Oct 21st 2011, 01:35 PM
SammyS
Re: taylor polynomial help!
Quote:

Originally Posted by Kuma
I don't really understand how to derive taylor polymomials for questions like these for example

find the 3rd degree taylor polymomial about the origin of
f(x,y) = (cos y) ln(xy+1)

Do you know the Taylor series for cos(x) and ln(1+1) ?
• Oct 21st 2011, 01:40 PM
Kuma
Re: taylor polynomial help!
yes. Do I just substitute the terms of the question into the taylor series of cos x and ln 1+x?

I was looking over some examples and that is what my instructor did. But what about a question like

cos(xy)/[1 + y^2]

there isn't a standard representation for the denominator.
• Oct 21st 2011, 01:46 PM
CaptainBlack
Re: taylor polynomial help!
Quote:

Originally Posted by Kuma
yes. Do I just substitute the terms of the question into the taylor series of cos x and ln 1+x?

I was looking over some examples and that is what my instructor did. But what about a question like

cos(xy)/[1 + y^2]

there isn't a standard representation for the denominator.

Expanding about $\displaystyle 0$:

$\displaystyle \frac{1}{1+y^2}=\frac{1}{1-(-y)^2}=1+(-y^2)+(-y^2)^2+...+(-y^2)^n+..$

CB