Question
Evaluate the left hand and right hand limits of the following function at $x=2$. Does $\lim _{x \rightarrow 2} f(x)$ exist ?
$
f(x)=\left\{\begin{array}{cll}
2 x+3, & \text { if } & x \leq 2 \\
x+5 & \text { if } & x>2
\end{array}\right.
$
$
f(x)=\left\{\begin{array}{cll}
2 x+3, & \text { if } & x \leq 2 \\
x+5 & \text { if } & x>2
\end{array}\right.
$