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## Homework Statement

Find the Taylor polynomial of degree 3 of [tex]\frac{1}{2+x-2y}[/tex] near (2,1).

## Homework Equations

## The Attempt at a Solution

I have already solved this problem by evaluating the R^2 Taylor series; I'm mostly curious about another aspect of the problem.

By substituting u = x-2y, it would seem that we can use the Maclaurin expansion of [tex]g(u) = \frac{1}{2+u}[/tex], and then substitute back to the original variables (since f(x,y) ~= g(u) when (x,y) ~= (2,1)) to get the relevant Taylor series for f(x,y).

I seem to be getting the wrong answer with this approach, but I'm curious why this is the case. Does this approach work under certain conditions for multivariable functions, or should it work in general if a relevant substitution can be made, indicating that I've made an arithmetical error somewhere?

Thanks.