Question

use the graph of h(x) shown below to evaluate lim h(x), if possible. if the limit does not exist, enter ∅.

Explanation:

Step1: Recall limit - definition

The limit $\lim_{x
ightarrow a}h(x)$ exists if and only if $\lim_{x
ightarrow a^{-}}h(x)=\lim_{x
ightarrow a^{+}}h(x)$, where $\lim_{x
ightarrow a^{-}}h(x)$ is the left - hand limit and $\lim_{x
ightarrow a^{+}}h(x)$ is the right - hand limit.

Step2: Analyze left - hand limit as $x

ightarrow0$
As $x$ approaches $0$ from the left side (values of $x$ less than $0$), the function $h(x)$ approaches $- 1$.

Step3: Analyze right - hand limit as $x

ightarrow0$
As $x$ approaches $0$ from the right side (values of $x$ greater than $0$), the function $h(x)$ approaches $-1$.

Answer:

$-1$