Define $f\left(x\right)=\frac{\cos x}{x}$ $ f:\mathbb{R\backslash}\left\{ 0\right\} \longrightarrow\mathbb{R}$
So I need to determine if there is a continuous extension to $f\left(x\right)$ at a=0 and then find it if so.
What I thought of is since ${\displaystyle \lim_{x\to a^{-}}f\left(x\right)=-\infty}$ and $ {\displaystyle \lim_{x\to a^{+}}f\left(x\right)=\infty}$ , then it's not possible that there is a continuous extension to $f\left(x\right)$
Is that argument valid?