How do you define $$\liminf_{x\to\infty} f(x) where $a>0$, and $f$ is continuous on $\mathbb R$?
Is it the following?
There exist $x_{0}$ such that $f(x) for all $x>x_{0}$
How do you define $$\liminf_{x\to\infty} f(x) where $a>0$, and $f$ is continuous on $\mathbb R$?
Is it the following?
There exist $x_{0}$ such that $f(x) for all $x>x_{0}$