Question

Math

Posted 3 months ago

```
Given the function $g$ and asked to estimate $\lim _{x \rightarrow 4} g(x)$, three students created tables.
Each table is accurate, but which one is the best for approximating the limit?
Choose 1 answer:
(A) \begin{tabular}{|ccccccc|}
\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}
$\mathrm{C}$ & $x$ & 3 & 3.5 & 3.75 & 3.95 & 3.999 \\
\hline & $g(x)$ & -4.25 & -4.375 & -4.438 & -4.498 & -4.5 \\
\hline
\end{tabular}
```

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To estimate $\lim_{x \rightarrow 4} g(x)$, we need to examine the values of $g(x)$ as $x$ approaches 4 from both sides

step 2

Table (A) provides values of $g(x)$ for $x$ approaching 4 from both sides: $3.9, 3.95, 3.999, 4.001, 4.05$. The values of $g(x)$ are $-4.475, -4.488, -4.5, -4.5, -4.513$

step 3

Table (B) provides values of $g(x)$ for $x$ approaching 4 from both sides: $-4.1, -4.05, -4.001, 4.001, 4.05, 4.1$. The values of $g(x)$ are $-5.525, -5.513, -5.5, -4.5, -4.513, -4.525$

step 4

Table (C) provides values of $g(x)$ for $x$ approaching 4 from one side: $3, 3.5, 3.75, 3.95, 3.999$. The values of $g(x)$ are $-4.25, -4.375, -4.438, -4.498, -4.5$

step 5

Comparing the tables, Table (A) is the best for approximating the limit because it provides values of $g(x)$ for $x$ approaching 4 from both sides and the values are closer to $-4.5$

Answer

Table (A)

Key Concept

Approximating Limits

Explanation

Table (A) provides the most accurate approximation of $\lim_{x \rightarrow 4} g(x)$ because it includes values of $g(x)$ for $x$ approaching 4 from both sides and the values are closest to the limit.

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