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You uploaded an image of the following limit expression:

\[
\lim_{x \to \infty} \frac{15x + 5}{12x^2 - 4x + 7}
\]

To solve this, let's analyze the behavior of the function as \( x \to \infty \).

### Step-by-step solution:

1. **Highest degree terms**: As \( x \) approaches infinity, the lower-degree terms become insignificant. We focus on the highest-degree terms in both the numerator and denominator.

   - The highest degree term in the numerator: \( 15x \)
   - The highest degree term in the denominator: \( 12x^2 \)

2. **Simplifying the expression**:
   \[
   \frac{15x + 5}{12x^2 - 4x + 7} \approx \frac{15x}{12x^2} = \frac{15}{12x}
   \]
   
   As \( x \to \infty \), \( \frac{15}{12x} \) approaches 0.

3. **Conclusion**:
   \[
   \lim_{x \to \infty} \frac{15x + 5}{12x^2 - 4x + 7} = 0
   \]

### Final Answer:
\[
\lim_{x \to \infty} \frac{15x + 5}{12x^2 - 4x + 7} = 0
\]

Would you like further explanation on any of these steps?

Here are 5 related questions to deepen your understanding:
1. What happens if the degrees of the numerator and denominator are the same?
2. How would the limit change if the highest degree terms in the numerator and denominator were swapped?
3. What is the limit of \( \frac{x}{x^2 + 1} \) as \( x \to \infty \)?
4. How can you use L'Hopital's Rule to solve this limit?
5. What if the function had a logarithmic

lim (x -> infinity) (15x + 5) / (12x^2 - 4x + 7)

Solve the limit of (15x + 5) / (12x^2 - 4x + 7) as x approaches infinity. Learn about rational functions, asymptotic behavior, and how to simplify expressions with higher-degree terms.

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