Consider the graph of function $g$. The dashed lines represent asymptotes.

Which limit expressions agree with the graph?
Choose all answers that apply:
A $\lim _{x \rightarrow 3} g(x)=\infty$
В $\lim _{x \rightarrow 3^{-}} g(x)=\infty$
() $\lim _{x \rightarrow 3^{+}} g(x)=\infty$

Question

Consider the graph of function $g$. The dashed lines represent asymptotes.

Which limit expressions agree with the graph?
Choose all answers that apply:
A $\lim _{x \rightarrow 3} g(x)=\infty$
В $\lim _{x \rightarrow 3^{-}} g(x)=\infty$
() $\lim _{x \rightarrow 3^{+}} g(x)=\infty$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the limit expressions that agree with the graph, we need to analyze the behavior of the function $g(x)$ as $x$ approaches 3 from different directions. ‖ ‖ step 2 ⋮ From the graph, as $x$ approaches 3 from the left ($x o 3^-$), $g(x)$ approaches positive infinity. Therefore, $\lim_{x o 3^-} g(x) = \infty$. ‖ ‖ step 3 ⋮ As $x$ approaches 3 from the right ($x o 3^+$), $g(x)$ approaches negative infinity. Therefore, $\lim_{x o 3^+} g(x) = -\infty$. ‖ ‖ step 4 ⋮ Since the limits from the left and right are not equal, the two-sided limit $\lim_{x o 3} g(x)$ does not exist. ‖ ***B*** ∻Key Concept∻ ⚹One-sided limits⚹ ∻Explanation∻ ⚹The behavior of the function $g(x)$ as $x$ approaches 3 from the left and right are different, leading to different one-sided limits.⚹◊What is the limit of the function $g(x)$ as $x$ approaches positive infinity based on the given information?⍭ Generate me a similar question◊

Sia