1. **State the problem:** Find the limit $$\lim_{x \to \infty} \frac{9}{4x^2 - 7}$$. 2. **Recall the rule for limits at infinity:** When the degree of the polynomial in the denominator is higher than in the numerator, the limit tends to zero. 3. **Analyze the expression:** The numerator is constant 9, and the denominator grows without bound as $$x^2$$ becomes very large. 4. **Evaluate the limit:** $$ \lim_{x \to \infty} \frac{9}{4x^2 - 7} = \frac{9}{\infty} = 0 $$ 5. **Conclusion:** The limit is 0 because the denominator grows much faster than the numerator.