Answer
False
Work Step by Step
We have to decide if the following statement is true:
$\displaystyle\lim_{x\rightarrow c^-}f(x)=\displaystyle\lim_{x\rightarrow c^+}f(x)$.
The one-sided limits are not always equal. For example:
$f(x)=\begin{cases}
x-1,\text{ if }x<1\\
2x,\text{ if }x\geq 1
\end{cases}$
We have:
$\displaystyle\lim_{x\rightarrow 1^-}f(x)=\displaystyle\lim_{x\rightarrow 1^-} (x-1)=0$
$\displaystyle\lim_{x\rightarrow 1^+}f(x)=\displaystyle\lim_{x\rightarrow 1^+} (2x)=2$
$0\not=2$
Therefore the statement is FALSE.
