Answer
1a. As $x$ approaches $a$, $f(x)$ approaches the value $L$.
1b. Yes
1c. $4$
Work Step by Step
1a. This is the fundamental definition of a limit. As $x$ approaches $a$, $f(x)$ approaches the value $L$.
1b. Although the limit says that $f(x)$ approaches $5$ when $x$ approaches $2$, this does not dictate the value of $f(2)$. For example, the function $f$ has a hole at $x = 2$ with the side limits equal to $5$ and the point $(2,3)$ also included included in the graph without consequence, meaning that $f(2)$ can equal $3$.
1c. As $x$ approaches $2$, $x^{2}$ approaches $4$. Therefore, $\displaystyle\lim_{x\to2} x^2 = 4$.
