The function $g$ is defined over the real numbers. This table gives select values of $g$.
\begin{tabular}{cc}
$x$ & $g(x)$ \
\hline-0.2 & 4.4 \
-0.02 & 3.14 \
-0.002 & 3.014 \
0 & 3 \
0.002 & 1250 \
0.02 & 125 \
0.2 & 13
\end{tabular}

What is a reasonable estimate for $\lim _{x ightarrow 0^{+}} g(x) ?$
Choose 1 answer:
(A) 0
(B) 3
(C) 1250
(D) Unbounded

Question

The function $g$ is defined over the real numbers. This table gives select values of $g$.
\begin{tabular}{cc}
$x$ & $g(x)$ \
\hline-0.2 & 4.4 \
-0.02 & 3.14 \
-0.002 & 3.014 \
0 & 3 \
0.002 & 1250 \
0.02 & 125 \
0.2 & 13
\end{tabular}

What is a reasonable estimate for $\lim _{x ightarrow 0^{+}} g(x) ?$
Choose 1 answer:
(A) 0
(B) 3
(C) 1250
(D) Unbounded

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the limit of $g(x)$ as $x$ approaches $0$ from the right, we need to examine the values of $g(x)$ as $x$ gets closer to $0$ from positive values. ‖ ‖ step 2 ⋮ From the table, the values of $g(x)$ for $x$ approaching $0$ from the right are: $g(0.002) = 1250$, $g(0.02) = 125$, and $g(0.2) = 13$. ‖ ‖ step 3 ⋮ As $x$ gets closer to $0$ from the right, $g(x)$ increases significantly, suggesting that $g(x)$ is becoming very large. ‖ ‖ step 4 ⋮ Therefore, the limit of $g(x)$ as $x$ approaches $0$ from the right is unbounded. ‖ ***D*** ∻Key Concept∻ ⚹Unbounded Limit⚹ ∻Explanation∻ ⚹When the values of a function increase without bound as the input approaches a certain point, the limit is considered unbounded.⚹◊What method can be used to estimate the limit of $g(x)$ as $x$ approaches 0 from the right based on the given data in the table?⍭ Generate me a similar question◊

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