Is it possible to use a Taylor expansion to approximate x2/x1?

Question

I have the expression $\frac{x_2}{x_1}$ which I would like to linearize, ie. ($a.x_2+b.x_1+...$). Can I use a Taylor expansion to do this?

Answer 1

Just have a look here for the development of Taylor series in several variables.

Applied to the case $$f(x,y)=\frac xy \qquad \text{around} \qquad x=a \qquad \text{and} \qquad y=b$$ the formula will give $$f(x,y)=\frac a b+\frac{1}b(x-a)-\frac{a }{b^2}(y-b)$$