I am working on some practice exercises on Taylor Polynomial and came across this problem:
Find the third order Taylor polynomial of $f(x,y)=x + \cos(\pi y) + x\log(y)$ based at $a=(3,1).$
In the solution provided, the author makes a substitution such that $x=3+h$ and $y=1+k$. I am not sure why he makes this substitution. Also, why not just find the Taylor polynomial for $f(x,y)$, then plug in the values for $x$ and $y$ to solve for $f(x,y)$?
If you could provide some references for reading on this I would appreciate that as well.
Thanks in advance.