## Calculus with Applications (10th Edition)

See: Existence of Limits ...3. If $\displaystyle \lim_{x\rightarrow a^{-}}f(x)=L$ and $\displaystyle \lim_{x\rightarrow a^{+}}f(x)=M$, and $L\neq M$, then $\displaystyle \lim_{x\rightarrow a}f(x)$ does not exist. $\displaystyle \lim_{x\rightarrow 2^{-}}f(x)\neq \displaystyle \lim_{x\rightarrow 2^{+}}f(x)$, so $\displaystyle \lim_{x\rightarrow 2}f(x)$ does not exist.