Question

use the graph of the function f shown to estimate the following limits and the function value. complete parts (a) through (d). (a) find the limit lim f(x) as x→ - 3. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. lim f(x) = (type an integer or a decimal.) b. the limit does not exist.

Explanation:

Step1: Analyze left - hand limit

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

Answer:

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