You should note that the higher order derivatives die off. Meaning are all zero. So it remains just to compute to get this Taylor series.
Hi,
I am currently looking over some revision questions from past papers and came across the following:
Compute all terms in the Taylor Series expansion of the function f(x,y)=x^2+y^2 (ie: x squared plus y squared) about the point (1,1).
Basically, here is where I am:
Write x=(x-1)+1 and y=(y-1)+1.
Then:
f(x,y)=((x-1)+1)^2+((y-1)+1)^2
= (x-1)^2+2(x-1)+1+(y-1)^2+2(y-1)+1
=(x-1)^2+(y-1)^2+2[(x-1)+(y-1)]+2.
I am then unsure what to do from here. Is this the end of the question? I cannot find a Taylor expansion which deals with (x-1) or (y-1) to write either of these as infinite series.
I would basically just like to know if there is anything else that is needed to finish answering the question, or is this done here? I thought about expanding the (x-1) and (y-1) terms, but surely then I will be going back to where I started from (ie: x^2+y^2).
Thanks for any help in advance.