Question

use the graph of h shown to the right to find the limit. if necessary, state that the limit does not exist. $lim_{x
ightarrow0}h(x)$ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x
ightarrow0}h(x)=square$ (simplify your answer.) b. the limit does not exist and is neither $infty$ nor $-infty$

Explanation:

Step1: Analyze left - hand limit

As \(x\) approaches \(0\) from the left side (\(x\to0^{-}\)), we observe the graph of \(H(x)\). Following the curve of the graph as \(x\) gets closer to \(0\) from the left, the \(y\) - value approaches \(6\).

Step2: Analyze right - hand limit

As \(x\) approaches \(0\) from the right side (\(x\to0^{+}\)), we follow the curve of the graph. As \(x\) gets closer to \(0\) from the right, the \(y\) - value approaches \(6\).

Step3: Determine the limit

Since the left - hand limit \(\lim_{x\to0^{-}}H(x) = 6\) and the right - hand limit \(\lim_{x\to0^{+}}H(x)=6\), then \(\lim_{x\to0}H(x)=6\).

Answer:

A. \(\lim_{x\to0}H(x)=6\)