I'm trying to understand this approximation:
$x \sqrt{\bigg(1+\alpha\Big(\frac{y}{x}-1\Big)\bigg)\bigg/\bigg(1+\alpha\Big(\frac{x}{y}-1\Big)\bigg)} \approx x\bigg(1+\frac{\alpha}{2}\Big(\frac{y}{x}-1-\frac{x}{y}+1\Big)\bigg)$
and this one:
$\Large\frac{(x^3 (1-\alpha)+y^3\alpha)\Big(\frac{(1-\alpha)}{x}+\frac{\alpha}{y}\Big)}{(x(1-\alpha)+y\alpha)^2}\approx 1+\alpha\frac{x}{y}\bigg(\frac{y^2}{x^2}-1\bigg)^2$
According to the brief explanation, we derive the approximation using Taylor series linearization.
I'm familiar with Taylor expansion of $f(x\pm ah)$, but not with linearization/approximation using Taylor.
I suspect there's some derivation involved, but I'm not too sure.
Can someone help?
