use the graph of h shown to the right to find the limit. if necessary, state that the limit does not exist…

use the graph of h shown to the right to find the limit. if necessary, state that the limit does not exist. $lim_{x\rightarrow0}h(x)$ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow0}h(x)=square$ (simplify your answer.) b. the limit does not exist and is neither $infty$ nor $-infty$

use the graph of h shown to the right to find the limit. if necessary, state that the limit does not exist. $lim_{x\rightarrow0}h(x)$ select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. $lim_{x\rightarrow0}h(x)=square$ (simplify your answer.) b. the limit does not exist and is neither $infty$ nor $-infty$

Answer

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)