To evaluate the limit \(\lim_{h \to -2} h^3 + 8h + 2\), substitute \(h = -2\) directly into the expression:

\[
h^3 + 8h + 2 \quad \text{when} \quad h = -2
\]

Calculate each term:

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

Now, sum these values:

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

So, the limit is:

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

Would you like further details or have any other questions?

Here are some related questions:
1. How do you evaluate limits involving more complex expressions?
2. What happens if the direct substitution in a limit leads to an indeterminate form?
3. How can you use the concept of limits to define continuity at a point?
4. What is the difference between one-sided and two-sided limits?
5. How do limits relate to derivatives in calculus?

**Tip:** Always check if direct substitution in a limit leads to a defined value or an indeterminate form, as this will guide your next steps.

Learn how to evaluate the limit \(\lim_{h \to -2} (h^3 + 8h + 2)\) step-by-step. This problem involves understanding limits and direct substitution in calculus, crucial for advanced high school students.

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