Subjects calculus

Limit Right 303F9A

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Limit Right 303F9A


1. The problem asks for a reasonable estimate of the right-hand limit of the function $g$ as $x$ approaches 0, i.e., $\lim_{x \to 0^+} g(x)$. 2. The right-hand limit means we consider values of $x$ that are positive and very close to 0. 3. From the table, the values of $g(x)$ for $x$ approaching 0 from the right are: - At $x=0.002$, $g(x)=1250$ - At $x=0.02$, $g(x)=125$ - At $x=0.2$, $g(x)=13$ 4. Notice that as $x$ gets closer to 0 from the right, $g(x)$ increases dramatically (from 13 to 125 to 1250). This suggests the function values are growing very large near 0 from the right side. 5. Since the values increase without bound as $x$ approaches 0 from the right, the limit is not a finite number but tends to infinity. 6. Therefore, the reasonable estimate for $\lim_{x \to 0^+} g(x)$ is that it is unbounded (infinite). Final answer: D Unbounded