Original picture:
LaTeX approximation:
$$f\color{blue}{\substack{(x)\\x\to\infty}}=\pm\sqrt{\frac{(x^2+x)^3}{\pi}}.$$ What does the notation highlighted in blue mean?
I understand that $x\to\infty$ means that $x$ is approaching infinity, but I do not understand how this could be used in a function.
I should probably confess that I first saw this while watching Spongebob... Even though this is a kids show I still don't see why the creators would make up nonsense mathematics. Here is a picture:
My guess is that $f(x)$ is a more complicated function, but that, as $x \to \infty$, $f(x)$ behaves like $\sqrt{\frac{(x^2+x)^3}{\pi}} $.
That can mean either $\dfrac{f(x)}{\sqrt{\frac{(x^2+x)^3}{\pi}}} \to 1 $ or $f(x)-\sqrt{\frac{(x^2+x)^3}{\pi}} \to 0 $.
I do not know what the "$\pm$" means, since the term following is monotonically increasing and unbounded.