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Question
Math
Posted 9 months ago

Given the function gg and asked to estimate lim⁡x→4g(x)\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 & xx & 3.9 & 3.95 & 3.999 & 4.001 & 4.05 \\
\hline & g(x)g(x) & -4.475 & -4.488 & -4.5 & -4.5 & -4.513 \\
\hline
\end{tabular}
(B) \begin{tabular}{|cccccccc|}
\hline B & xx & -4.1 & -4.05 & -4.001 & 4.001 & 4.05 & 4.1 \\
\hline & g(x)g(x) & -5.525 & -5.513 & -5.5 & -4.5 & -4.513 & -4.525 \\
\hline
\end{tabular}
(C) \begin{tabular}{ccccccc}
C\mathrm{C} & xx & 3 & 3.5 & 3.75 & 3.95 & 3.999 \\
\hline & g(x)g(x) & -4.25 & -4.375 & -4.438 & -4.498 & -4.5 \\
\hline
\end{tabular}
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Answer from Sia
Posted 9 months ago
Solution by Steps
step 1
To estimate lim⁡x→4g(x)\lim_{x \rightarrow 4} g(x), we need to examine the values of g(x)g(x) as xx approaches 4 from both sides
step 2
Table (A) provides values of g(x)g(x) for xx approaching 4 from both sides: 3.9,3.95,3.999,4.001,4.053.9, 3.95, 3.999, 4.001, 4.05. The values of g(x)g(x) are −4.475,−4.488,−4.5,−4.5,−4.513-4.475, -4.488, -4.5, -4.5, -4.513
step 3
Table (B) provides values of g(x)g(x) for xx approaching 4 from both sides: −4.1,−4.05,−4.001,4.001,4.05,4.1-4.1, -4.05, -4.001, 4.001, 4.05, 4.1. The values of g(x)g(x) are −5.525,−5.513,−5.5,−4.5,−4.513,−4.525-5.525, -5.513, -5.5, -4.5, -4.513, -4.525
step 4
Table (C) provides values of g(x)g(x) for xx approaching 4 from one side: 3,3.5,3.75,3.95,3.9993, 3.5, 3.75, 3.95, 3.999. The values of g(x)g(x) are −4.25,−4.375,−4.438,−4.498,−4.5-4.25, -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)g(x) for xx approaching 4 from both sides and the values are closer to −4.5-4.5
Answer
Table (A)
Key Concept
Approximating Limits
Explanation
Table (A) provides the most accurate approximation of lim⁡x→4g(x)\lim_{x \rightarrow 4} g(x) because it includes values of g(x)g(x) for xx approaching 4 from both sides and the values are closest to the limit.

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