Question

If $f\left(x\right)=\{\begin{array}{cc}2,& x>4\\ 0,& x\le 4\end{array}$ then $\underset{x\to 4}{lim}f\left(x\right)$ equals to

• A. $0$
• B. $2$
• C. does not exist
• D. none of these

Answer 1

The correct option is C does not exist

Left hand limit $=\underset{x\to 4^{-}}{lim}f\left(x\right)=0$

and Right hand limit $=\underset{x\to 4^{+}}{lim}f\left(x\right)=2$

Clearly $\text{Left hand limit}\ne \text{Right hand limit}$

Hence $\underset{x\to 4}{lim}f\left(x\right)$ does not exist.