9 mark for review the table above gives selected values for a function f. also shown is a portion of the…

Explanation:

Step1: Recall limit definition

The limit $\lim_{x\rightarrow a}f(x)$ exists if the left - hand limit $\lim_{x\rightarrow a^{-}}f(x)$ and the right - hand limit $\lim_{x\rightarrow a^{+}}f(x)$ are equal.

Step2: Find left - hand limit

As $x$ approaches $3$ from the left ($x\rightarrow3^{-}$), we look at the values of $f(x)$ for $x = 2.9,2.95,2.98,2.999$. From the table, as $x$ gets closer to $3$ from the left, $f(x)$ approaches $1.6$.

Step3: Find right - hand limit

As $x$ approaches $3$ from the right ($x\rightarrow3^{+}$), we look at the values of $f(x)$ for $x = 3.001,3.02,3.05,3.1$. From the table, as $x$ gets closer to $3$ from the right, $f(x)$ approaches $1.6$.

Step4: Determine the limit

Since $\lim_{x\rightarrow3^{-}}f(x)=\lim_{x\rightarrow3^{+}}f(x) = 1.6$, then $\lim_{x\rightarrow3}f(x)=1.6$.

Answer:

A. 1.6