Question

decide from the graph whether a limit exists. if a limit exists, find its value. lim f(x) x→3 what is the limit? select the correct choice below and fill in any answer boxes in your choice. a. the limit is the real number b. the limit does not exist.

Explanation:

Step1: Observe left - hand limit

As $x$ approaches $3$ from the left side ($x\to3^{-}$), the function values approach the same value as when approaching from the right.

Step2: Observe right - hand limit

As $x$ approaches $3$ from the right side ($x\to3^{+}$), the function values approach the value of the function at $x = 3$.

Step3: Determine the limit

Since the left - hand limit and the right - hand limit are equal, the limit exists. Looking at the graph, when $x = 3$, $F(x)=1$.

Answer:

A. The limit is the real number $1$