## Precalculus (6th Edition) Blitzer

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."
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.