Answer
The correct fill for the blank provided in the statement is $ f\left( a \right)$.
Work Step by Step
In case of a polynomial function, for any value of $ a $, as $ x $ gets closer to $ a $, the limit of the polynomial is the polynomial evaluated at $ a $. That is,
The limit of a polynomial:
If $ f $ is a polynomial function, then
$\underset{x\to a}{\mathop{\lim }}\,\text{ }f\left( x \right)=f\left( a \right)$
Where $ a $ is a number.
The limit of a polynomial is the polynomial evaluated at $ a $ as $ x $ approaches $ a $.
For example:
Let $ f\left( x \right)=x $,
$\underset{x\to 7}{\mathop{\lim }}\,f\left( x \right)=\underset{x\to 7}{\mathop{\lim }}\,x=7$
Therefore, the correct fill for the blank provided in the statement is $ f\left( a \right)$.
