I'm trying to figure out how to get this result via taylor expansion as $x,y \rightarrow \infty$:
$f(x) = \sqrt{(x-1)y} = \sqrt{xy} - \frac{1}{2}\sqrt{\frac{y}{x}} + ...$
I've been told (on yahoo answers), that since you can't take taylor expansions at infinity, you do it on intervals (what does that mean?). Specifically, I was told:
You can write
f(x) = f(a) + (x-a) f'(a) + error term
or
f(a) = f(x) -(x-a)f'(x) + error term
Here your 2 ends are X and X - 1
I'm not sure what that means =P.
I am looking for a step-by-step taylor series calculation up to the first 2 terms. I've never approximated a function "at infinity" nor am I familiar with the generalized formula for taylor expansion.
So, any help would be great.
Thanks!