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

Explanation:

Step1: Recall the concept of the limit of a function.

The limit $\lim_{x\rightarrow3}f(x)$ exists if and only if $\lim_{x\rightarrow3^{-}}f(x)=\lim_{x\rightarrow3^{+}}f(x)$.

Step2: Analyze the left - hand limit.

As $x$ approaches $3$ from the left ($x\rightarrow3^{-}$), we look at the values of $f(x)$ for $x = 2.9,2.95,2.98,2.999$. The values of $f(x)$ are approaching $1.6$.

Step3: Analyze the right - hand limit.

As $x$ approaches $3$ from the right ($x\rightarrow3^{+}$), we look at the values of $f(x)$ for $x=3.001,3.02,3.05,3.1$. The values of $f(x)$ are approaching $1.6$.

Step4: Determine the limit.

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

Answer:

A. 1.6