Subjects calculus

Limit Approximation 40Dfa3

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1. The problem asks why choice C is wrong regarding the appropriateness of the table for approximating $\lim_{x \to -6} h(x)$. 2. Choice C states: "The table isn't appropriate. The increments in x-values are constant." 3. To understand this, recall that when approximating limits from tables, constant increments in $x$ are not a problem. In fact, having evenly spaced $x$-values helps in observing the behavior of the function near the point of interest. 4. The key issue in limit approximation is whether the $x$-values approach the limit point from both sides (left and right). Constant increments do not prevent this. 5. In the given table, $x$ values go from $-9$ to $-3$ in increments of 1, so they approach $-6$ only from the left side (values less than $-6$). There are no $x$ values greater than $-6$ to approach from the right side. 6. Therefore, the problem with the table is not the constant increments but the lack of $x$ values approaching $-6$ from both sides. This makes choice C incorrect. Final answer: Choice C is wrong because constant increments in $x$ do not make the table inappropriate for limit approximation; the real issue is the one-sided approach to $-6$.