I have the function:
$f(x) = \frac{5}{(1+x^2)(2+x)}$
How do I find the first n terms in the expansion of f(x) if $x$ is large?
I have no issue in finding it if x is small - we convert it into partial fraction first, then expand as usual.
What is the difference between if x is large and x is small anyway?
P.S. I am new here, still figuring out how to use math jax
When $x$ is small, you can view your fraction as $\frac 5{2+correction terms}$ because all the terms with a factor $x$ are small. When $x$ is large you can view your fraction as $\frac 5{x^3+correction terms}$ because terms with lower powers of $x$ are much smaller. For large $x$ you can factor out $\frac 5{x^3}$ then expand in powers of $\frac 1x$. You do this because $\frac 1x$ is small.