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We are tasked with finding the limit:

\[
\lim_{x \to \infty} 8 \cos \left( \frac{6}{5x} \right)
\]

### Step-by-step solution:

1. As \(x\) approaches infinity, the term \(\frac{6}{5x}\) approaches zero because:
   \[
   \lim_{x \to \infty} \frac{6}{5x} = 0
   \]
2. The cosine function is continuous, so we can take the limit inside the cosine function:
   \[
   \lim_{x \to \infty} \cos \left( \frac{6}{5x} \right) = \cos(0)
   \]
3. We know that \(\cos(0) = 1\).
4. Now multiply the result by the constant 8:
   \[
   8 \cdot 1 = 8
   \]

Thus, the correct limit is:

\[
\boxed{8}
\]

Let me know if you'd like further details or have any questions. 

Here are five related questions you might explore:
1. What is the limit of \(\cos \left( \frac{1}{x} \right)\) as \(x \to \infty\)?
2. What happens if we replace the cosine function with sine in the original problem?
3. How does the limit of exponential functions compare with trigonometric functions as \(x \to \infty\)?
4. Can you solve a similar limit involving \(\sin\) instead of \(\cos\)?
5. How would the limit change if the expression inside the cosine function had a different power of \(x\)?

**Tip**: When solving limits involving trigonometric functions, consider using limit laws and the continuity of the trigonometric function to simplify the expression.

Find the limit of 8 * cos(6 / 5x) as x approaches infinity.

Learn how to find the limit of 8 * cos(6 / 5x) as x approaches infinity. This calculus problem involves the application of limit laws and the continuity of trigonometric functions. The correct limit is 8. Suitable for high school and college students studying calculus.

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