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The given limit is:

\[
\lim_{x \to \infty} \frac{24x^{14} + 18}{8x^{14} + x^8}
\]

### Steps to solve:

1. **Analyze the degree of the terms**: The highest degree in both the numerator and denominator is \(x^{14}\).

2. **Divide both the numerator and denominator by \(x^{14}\)** (the highest power of \(x\)):

\[
\frac{24x^{14} + 18}{8x^{14} + x^8} = \frac{24 + \frac{18}{x^{14}}}{8 + \frac{1}{x^6}}
\]

3. **Simplify the limit as \(x \to \infty\)**:
   - As \(x \to \infty\), \(\frac{18}{x^{14}} \to 0\) and \(\frac{1}{x^6} \to 0\).
   - This simplifies the expression to:

\[
\frac{24 + 0}{8 + 0} = \frac{24}{8} = 3
\]

### Final Answer:
\[
\boxed{3}
\]

Would you like more details on this solution, or do you have any questions?

Here are 5 related questions:
1. What happens if the highest power of \(x\) in the denominator is greater than in the numerator?
2. How does dividing by the highest power of \(x\) help simplify limits?
3. What other methods can be used to solve limits at infinity?
4. Can this method be applied to limits involving exponential functions?
5. How would the limit change if the power of \(x\) in the numerator and denominator were different?

**Tip:** When dealing with limits at infinity, always look at the highest degree term to dominate the behavior of the function.

Find the limit: lim (x → ∞) (24x^14 + 18) / (8x^14 + x^8).

Learn how to find the limit of (24x^14 + 18) / (8x^14 + x^8) as x approaches infinity. This step-by-step solution shows how to divide by the highest degree term and simplify the limit using algebraic principles. Suitable for high school students in Grades 11-12.

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