limh→−2h3+8h+2=


Pregunta 2Respuesta

A.
−∞



B.
0



C.
16



D.
8



E.
12

Let's re-evaluate the expression to ensure accuracy:

We want to find the limit:

\[
\lim_{h \to -2} \left(h^3 + 8h + 2\right)
\]

Substitute \( h = -2 \) directly into the expression:

1. \( h^3 = (-2)^3 = -8 \)
2. \( 8h = 8(-2) = -16 \)
3. The constant term is \( +2 \)

Now, sum these values:

\[
-8 + (-16) + 2 = -24 + 2 = -22
\]

However, the answers provided do not match \(-22\). Let's reconsider the expression:

Given the multiple-choice answers and rechecking, it's likely there's a mistake in the interpretation or problem. Could you please verify if the expression or options were correct, or confirm if the problem should be interpreted differently?

Based on direct calculation:

\[
\lim_{h \to -2} \left(h^3 + 8h + 2\right) = -22
\]

Which does not match any of the given options.

Let me know how you'd like to proceed, or if there was a different expression intended.

Here are some related questions:
1. How can limits be used to analyze the behavior of functions near points?
2. What are common errors when solving limits, and how can they be avoided?
3. How do different forms of limits (e.g., infinite limits) differ in interpretation?
4. When should L'Hôpital's rule be applied to evaluate limits?
5. How are limits used in real-world applications, such as physics or engineering?

**Tip:** Always double-check your calculations and assumptions, especially when working with limits, as small mistakes can lead to incorrect conclusions.

Explore how to evaluate the limit of the expression h^3 + 8h + 2 as h approaches -2 with a detailed step-by-step solution. This problem involves applying limit theorems and is suitable for advanced high school students.

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