Let say we have a function:
$$f(n) = n^2 + 2n + 5 $$
According to wiki, limiting behavior of f(n) is:
$$n^2 + 2n + 5 \sim n^2 \space (as \space n \space \rightarrow \infty) $$
For example we have a function g(n):
$$g(n) = 5n^3 + n$$
I'm confused what is the limiting behavior of g(n):
$$5n^3 + n \sim 5n^3 \space (as \space n \space \rightarrow \infty) $$
or just simply (without a constant 5):
$$5n^3 + n \sim n^3 \space (as \space n \space \rightarrow \infty) $$
If latter is true, could you please explain why we drop the 5 constant?