Question

use the graph of the function f shown to the right to estimate the indicated function values and limits. complete (a) through (e). (a) find the value of lim f(x). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim f(x)=□ b. the limit does not exist.

Explanation:

Step1: Analyze left - hand limit

As \(x\) approaches \(- 2\) from the left side (\(x\to - 2^{-}\)), we look at the part of the graph where \(x\) values are less than \(-2\) and getting closer to \(-2\). By observing the graph, we see that the \(y\) - values approach \(3\).

Step2: Analyze right - hand limit

As \(x\) approaches \(- 2\) from the right side (\(x\to - 2^{+}\)), we look at the part of the graph where \(x\) values are greater than \(-2\) and getting closer to \(-2\). By observing the graph, we see that the \(y\) - values approach \(3\).
Since the left - hand limit and the right - hand limit as \(x\) approaches \(-2\) are equal.

Answer:

A. \(\lim_{x\to - 2}f(x)=3\)