Answer
The complete statement is, “The notation $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=L $ means that as x gets closer to a, but remains unequal to a, the corresponding value of $ f\left( x \right)$ gets closer to L."
Work Step by Step
Consider the provided limit notation, $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=L $
Here, $ f $ is any function defined on some open interval containing the number $ a $.
The function $f$ may or may not defined at a.
The notation $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=L $ is read as: the limit of $ f\left( x \right)$ as x approaches a is equal to the number L.
Hence, the notation $\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)=L $ means that as x gets closer to a, but remains unequal to a, the corresponding value of $ f\left( x \right)$ gets closer to L.
