Question

use the graph to evaluate the limit. lim f(x) x→0 -1 does not exist ∞ 1

Explanation:

Step1: Recall limit definition

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

Step2: Find left - hand limit

As $x$ approaches $0$ from the left side ($x
ightarrow0^{-}$), looking at the graph, the value of $y = f(x)$ approaches $1$.

Step3: Find right - hand limit

As $x$ approaches $0$ from the right side ($x
ightarrow0^{+}$), looking at the graph, the value of $y = f(x)$ approaches $1$.

Step4: Determine the limit

Since $\lim_{x
ightarrow0^{-}}f(x)=\lim_{x
ightarrow0^{+}}f(x) = 1$, then $\lim_{x
ightarrow0}f(x)=1$.

Answer:

1