Limit Approaching Infinity Definition

${\lim }_{x\to \infty }f(x)=L$ where $L\in R$. Use $ϵ$ or for y-axis use $\delta$ or for x-axis This means that $x$ large $⟹$ $f(x)$ close to L for $f(x)$ to be close to $L$, then $|f-L|<ϵ$ (the distance between them) should be close to 0. For $x$ to be large, $x>\delta$ So, it is : $\forall ϵ>0,\exists N>0$ such that $x>\delta ⟹|f-L|<ϵ$