review the graph of function h(x). what is the limit, if it exists? lim h(x) as x→2 0 1 3 dne

Explanation:

Step1: Recall limit - definition

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

Step2: Find left - hand limit as $x\rightarrow2$

As $x$ approaches $2$ from the left side ($x\rightarrow2^{-}$), following the graph of $h(x)$, the $y$ - values approach $0$.

Step3: Find right - hand limit as $x\rightarrow2$

As $x$ approaches $2$ from the right side ($x\rightarrow2^{+}$), following the graph of $h(x)$, the $y$ - values approach $- 4$.

Step4: Compare left - and right - hand limits

Since $\lim_{x\rightarrow2^{-}}h(x)=0$ and $\lim_{x\rightarrow2^{+}}h(x)=-4$, and $0\neq - 4$.

Answer:

DNE