Question

use the graph of g(x) to evaluate $\lim\limits_{x \to 5^+} g(x)$ (options: $\infty$, does not exist, $-3$, $1$)

Explanation:

Step1: Understand Right-Hand Limit

The right - hand limit $\lim_{x
ightarrow a^{+}}g(x)$ is the value that $g(x)$ approaches as $x$ gets closer to $a$ from the right - hand side (values of $x$ greater than $a$).

Step2: Analyze the Graph for $x

ightarrow5^{+}$
From the graph, as $x$ approaches $5$ from the right (moving along the $x$ - axis towards $5$ from values like $5.1,5.01,5.001,\cdots$), we observe the behavior of the function $g(x)$. The graph shows that as $x$ approaches $5$ from the right, the function values seem to approach $1$. We check the options: $\infty$ would be the case if the function was increasing without bound near $x = 5$ from the right, but the graph doesn't show that. "Does not exist" is not correct here as we can see a clear trend. $- 3$ is not the value the function approaches from the right.

Answer:

D. 1 (assuming the options are labeled as A. $\infty$, B. Does not exist, C. - 3, D. 1)