Given the function $g$ and asked to estimate $\lim _{x ightarrow 4} g(x)$, three students created tables.

Each table is accurate, but which one is the best for approximating the limit?

Choose 1 answer:
(A) \begin{tabular}{|crccccc|}
\hline A & $x$ & 3.9 & 3.95 & 3.999 & 4.001 & 4.05 \
\hline & $g(x)$ & -4.475 & -4.488 & -4.5 & -4.5 & -4.513 \
\hline
\end{tabular}
(B) \begin{tabular}{|cccccccc|}
\hline B & $x$ & -4.1 & -4.05 & -4.001 & 4.001 & 4.05 & 4.1 \
\hline & $g(x)$ & -5.525 & -5.513 & -5.5 & -4.5 & -4.513 & -4.525 \
\hline
\end{tabular}
(C) \begin{tabular}{|ccccccc|}
\hline $\mathrm{C}$ & $x$ & 3 & 3.5 & 3.75 & 3.95 & 3.999 \
\hline & $g(x)$ & -4.25 & -4.375 & -4.438 & -4.498 & -4.5 \
& & & & & &
\end{tabular}

Question

Given the function $g$ and asked to estimate $\lim _{x ightarrow 4} g(x)$, three students created tables.

Each table is accurate, but which one is the best for approximating the limit?

Choose 1 answer:
(A) \begin{tabular}{|crccccc|}
\hline A & $x$ & 3.9 & 3.95 & 3.999 & 4.001 & 4.05 \
\hline & $g(x)$ & -4.475 & -4.488 & -4.5 & -4.5 & -4.513 \
\hline
\end{tabular}
(B) \begin{tabular}{|cccccccc|}
\hline B & $x$ & -4.1 & -4.05 & -4.001 & 4.001 & 4.05 & 4.1 \
\hline & $g(x)$ & -5.525 & -5.513 & -5.5 & -4.5 & -4.513 & -4.525 \
\hline
\end{tabular}
(C) \begin{tabular}{|ccccccc|}
\hline $\mathrm{C}$ & $x$ & 3 & 3.5 & 3.75 & 3.95 & 3.999 \
\hline & $g(x)$ & -4.25 & -4.375 & -4.438 & -4.498 & -4.5 \
& & & & & &
\end{tabular}

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ We are given three tables and asked to estimate $ \lim_{x \rightarrow 4} g(x) $. We need to determine which table provides the best approximation. ‖ ‖ step 2 ⋮ Table A: $x = 3.9, 3.95, 3.999, 4.001, 4.05$ and $g(x) = -4.475, -4.488, -4.5, -4.5, -4.513$ ‖ ‖ step 3 ⋮ Table B: $x = -4.1, -4.05, -4.001, 4.001, 4.05, 4.1$ and $g(x) = -5.525, -5.513, -5.5, -4.5, -4.513, -4.525$ ‖ ‖ step 4 ⋮ Table C: $x = 3, 3.5, 3.75, 3.95, 3.999$ and $g(x) = -4.25, -4.375, -4.438, -4.498, -4.5$ ‖ ‖ step 5 ⋮ To find the best approximation, we look for the table where $g(x)$ values are closest to each other as $x$ approaches 4. ‖ ‖ step 6 ⋮ Table A shows $g(x)$ values converging to $-4.5$ as $x$ approaches 4. ‖ ‖ step 7 ⋮ Table B has a wider range of $x$ values and $g(x)$ values are not as consistent. ‖ ‖ step 8 ⋮ Table C also shows $g(x)$ values converging to $-4.5$, but it has fewer points near $x = 4$. ‖ ‖ step 9 ⋮ Therefore, Table A provides the best approximation for $ \lim_{x \rightarrow 4} g(x) $. ‖ ***A*** ∻Key Concept∻ ⚹Approximating Limits Using Tables⚹ ∻Explanation∻ ⚹The best table for approximating a limit is the one where the function values are most consistent and closest to the limit as the variable approaches the given point.⚹◊What is the formula for estimating a limit using data tables⍭ Generate me a similar question◊

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