
Taylor expansion
Hi guys, my lecturer recently did this in class and told us to check it ourselves but I'm having trouble.
We have the solution
$\displaystyle
A_{a,b} = \frac{\beta + 2\alpha^2  2\alpha \pm \sqrt{\beta^2  4 \beta (1\alpha)}}{2(\alpha^2 +\beta)}
$
making sense only if $\displaystyle \beta > 4(1\alpha).$
He then writes Taylor expanding as $\displaystyle \beta \to \infty$
$\displaystyle A_a = 1\frac{1}{\beta}+O\left(\frac{1}{\beta^2}\right)$
$\displaystyle A_b = \frac{(\alpha1)^2}{\beta}$
Which I just cannot seem to understand. Any help in understanding would be greatly appreciated,
thanks,
James