# calculus and analysis – Series expansion for two limits of x

I have a function f($$x$$) given by the expression

$$f (x) = frac{left(1+xleft(1-sqrt{1+x^2}right)right)^2-x+x^3left(1-sqrt{1+x^2}right)^2}{1+x^2left(1-sqrt{1+x^2}right)^2}$$

and would like to expand it for two limits of $$x$$: $$x gg 1$$ and $$x ll 1$$. From the posts I’ve read here, there seems to be a simple ‘command’ to do so in Mathematica:

$$x gg 1 longrightarrow text{Series}left(f(x),{x,text{Infinity},4}right)$$

$$x ll 1 longrightarrow text{Series}left(f(x),{x,0,4}right)$$

Since I am quite new to this, I am a bit confused about how this works. Why is it that for $$x gg 1$$ we consider Infinity, and for the other limit we consider $$x = 0$$? From the documentation, Series ‘generates a power series expansion for f about the point x=x0’, and I cannot understand why this is the same as our situation.