Answer
The correct fill for the blank provided in the expression “$\underset{x\to a}{\mathop{\lim }}\,\text{ }c=$______” is $\underset{x\to a}{\mathop{\lim }}\,\text{ }c=c $.
Work Step by Step
The limits involving a constant function give the same constant as the result. That is:
For the constant function $ f\left( x \right)=c $,
$\begin{align}
& \underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=\underset{x\to a}{\mathop{\lim }}\,\text{ }c \\
& =c
\end{align}$
Where $ a $ is any number.
The limit of any constant is that constant regardless of what number $ x $ approaches.
Therefore, the correct fill for the blank provided in the expression “$\underset{x\to a}{\mathop{\lim }}\,\text{ }c=$______” is $\underset{x\to a}{\mathop{\lim }}\,\text{ }c=c $.
